Ken White (Popehat) summarizes them, and, with his permission, I'm including the body of his analysis below:
Kavanaugh has been an appellate judge for 12 years and has written many opinions on free speech issues. They trend very protective of free speech, both in substance and in rhetoric. His opinions are consistent with the Supreme Court's strong protection of free speech rights this century. People who buy into the "conservatives are weaponizing the First Amendment" narrative will see him as a strong advocate of that movement, in that he has applied the First Amendment to campaign finance laws, telecommunications regulation, and other aspects of the regulatory state. But he's also demonstrated fidelity to free speech principles in classic speech scenarios. Even when he concurs in a First Amendment decision, he frequently writes a separate opinion to clarify his analytical approach to the problem. He's quoted First Amendment guru Eugene Volokh — one of the leading voices in free speech analysis and a strong defender of speech rights.
Free Speech and Elections Law. Kavanaugh has voted to strike down campaign financing laws and regulations under the First Amendment. Because he's a judge on the D.C. Circuit, which tends to get cases challenging federal regulations, he's done so multiple times. In Emily's List v. Fed. Election Comm'n, 581 F.3d 1, 4 (D.C. Cir. 2009), he ruled in favor of the progressive EMILY's List, striking down the Federal Election Commission's regulations of political expenditures by nonprofits. He concurred wtihout writing a separate opinion in Pursuing America's Greatness v. Fed. Election Comm'n, 831 F.3d 500, 510–11 (D.C. Cir. 2016), which struck down an FEC regulation prohibiting unauthorized political committees from using candidates' names in the titles of their web sites and social media pages.
Classic Speech Scenarios. In cases involving "classic free speech scenarios" — the sort of thing that's not derided as "weaponizing the First Amendment" — Kavanaugh has applied the First Amendment vigorously to protect speech. In Initiative & Referendum Inst. v. U.S. Postal Serv., 794 F.3d 21, 24 (D.C. Cir. 2015), he ruled that a Postal Service regulation that barred collecting signatures outside of post offices chilled speech and violated the First Amendment even though the Postal Service had stopped enforcing it. In Boardley v. U.S. Dep't of Interior, 615 F.3d 508, 523–24 (D.C. Cir. 2010), he wrote a strong concurring opinion in a case that struck down a National Park Service regulation requiring a permit for demonstrations on national park grounds, in which he focused both on the burden on speakers and the right to protest anonymously. On the other hand, Kavanaugh has not hesitated to apply traditional First Amendment exceptions when supported by the record. For instance, in Al Bahlul v. United States, 767 F.3d 1, 75–76 (D.C. Cir. 2014), he agreed that Al Qaeda recruitment videos aimed at inciting viewers to kill Americans were not protected under the classic Brandenburg test because they were directed to inciting and likely to incite imminent lawless action. (This led him to quote the somewhat infamous "the Constitution is not a suicide pact" line, one of my least favorite First Amendment rhetorical tropes.) And in Mahoney v. Doe, 642 F.3d 1112, 1114 (D.C. Cir. 2011), he took a somewhat you-kids-off-my-lawn tone in a concurring opinion agreeing that the government could prohibit "defacing government property" — in this case, by chalking sidewalks outside the White House — so long as it did so in a way that was neutral as to subject matter and viewpoint.
Commercial Speech. Courts treat "commercial speech" as somewhat less protected than other speech; the scope of that carve-out is a matter of dispute. Kavanaugh's opinions suggest that the "commercial speech" doctrine should be interpreted narrowly and in favor of speech. For instance, in Am. Meat Inst. v. U.S. Dep't of Agric., 760 F.3d 18, 30–32 (D.C. Cir. 2014), he wrote a concurring opinion offering a more narrow grounds for upholding a regulation requiring labeling of foreign-made goods. He rejected the government's broad argument that it had a substantial interest in forcing vendors to inform customers of the foreign origin of goods, because doing so is not tied to avoiding deception or promoting health and safety. He accepted the government's narrower argument that it had a substantial interest in promoting American-made goods.
Government Speech. The government is allowed to regulate speech on its own behalf; when the message is from and by the government it can determine its content in a way it cannot when it's someone else's speech. The government frequently invokes this doctrine at the margins to defend speech regulation — for instance, in Matal v. Tam, the government argued unsuccessfully that it could ban "offensive" trademarks because issuing a trademark is government speech. Judge Kavanaugh reads government speech fairly broadly. In DKT Int'l, Inc. v. U.S. Agency for Int'l Dev., 477 F.3d 758, 764 (D.C. Cir. 2007), he agreed that the government could fund only those NGOs that adopted a message of anti-sex-trafficking on the grounds that the government could fund the message it chose. In Bryant v. Gates, 532 F.3d 888, 898 (D.C. Cir. 2008), he wrote that the government could restrict who can advertise in military newspapers because such papers are government speech.
Net Neutrality and Telecommunications Regulation. Oh, people will flip out over this one. In short, Kavanaugh believes in applying the First Amendment to telecommunications regulation. He's written in numerous opinions that the government can't restrict the "editorial discretion" of internet service providers or content networks absent a showing that a particular provider "possesses market power in a relevant geographic market." Put another way, he believes that the First Amendment prohibits the government from telling ISPs and other communications providers that they have to carry competitor's content unless the government's made a showing that they have an anti-competitive level of power in a market. He's blunt about it. "[T]he net neutrality rule violates the First Amendment to the U.S. Constitution," he wrote in one dissent, pointing out that the government had not even tried to make a market power argument to support the regulation in that case. United States Telecom Ass'n v. Fed. Commc'ns Comm'n,855 F.3d 381, 418 (D.C. Cir. 2017). In Comcast Cable Commc'ns, LLC v. F.C.C., 717 F.3d 982, 994 (D.C. Cir. 2013), he wrote a concurring opinion emphasizing that the FCC could not tell Comcast or other programming distributors what content to carry absent a showing of market power requiring it. "[T]he FCC cannot tell Comcast how to exercise its editorial discretion about what networks to carry any more than the Government can tell Amazon or Politics and Prose or Barnes & Noble what books to sell; or tell the Wall Street Journal or Politico or the Drudge Report what columns to carry; or tell the MLB Network or ESPN or CBS what games to show; or tell SCOTUSblog or How Appealing or The Volokh Conspiracy what legal briefs to feature." He sounded similar notes in his dissent in Cablevision Sys. Corp. v. F.C.C., 597 F.3d 1306, 1316 (D.C. Cir. 2010) Put another way, Kavanaugh is unwilling to assume that the goal of competition justifies regulating what content networks must provide absent specific evidence of anti-competitive circumstances.
Limited To Textual and Historical Grounds. Kavanaugh has declined to find new rights within the First Amendment. For instance, in We the People Found., Inc. v. United States, 485 F.3d 140, 141 (D.C. Cir. 2007), he agreed that the First Amendment's right to petition the government does not carry with it a right to have the government respond.
Unions. After Janus, everybody's arguing that judges have "weaponized" the First Amendment against unions, so it's worthwhile to note a union case. In Venetian Casino Resort, L.L.C. v. N.L.R.B., 793 F.3d 85, 87–88 (D.C. Cir. 2015), Kavanaugh wrote that an employer did not violate the National Labor Relations Act by calling the cops on a union protest on its premises. This was a fairly straightforward application of something called the Noerr–Pennington doctrine, which says that behavior doesn't violate federal antitrust or labor law when it amounts to petitioning the government as protected by the First Amendment. This was an unremarkable application of that doctrine. Kavanaugh noted that other conduct by the employer could violate the NLRA, and remanded the case for a determination of whether an exception for "sham petitions" applied, so it takes effort to force this into an "anti-union" narrative.
Discrimination and Employment. Kavanaugh applies, in a straightforward fashion, existing doctrines limiting lawsuits claiming discrimination or retaliation based on speech. For instance, in LeFande v. D.C., 841 F.3d 485, 496–97 (D.C. Cir. 2016), he agreed that the standard Pickering-Connick "balancing test" for whether a government employee's speech is protected permitted a police department to fire a cop for derogatory emails sent to supervisors. In Moore v. Hartman, 704 F.3d 1003, 1004 (D.C. Cir. 2013), he agreed that the law was unsettled about whether an arrest in retaliation for speech is insulated from suit when there is probable cause for the arrest, and therefore the officers enjoyed qualified immunity because the right was not "clearly established." (Notably, the Supreme Court just accepted cert to resolve that question of law.) This application of existing doctrine, though unremarkable, has the impact of making it more difficult to vindicate free speech rights.
Defamation and Anti-SLAPP. Kavanaugh has applied familiar First Amendment doctrine to limit defamation suits, and in doing so has explicitly recognized that defamation litigation can chill speech. In 2017 he wrote "[t]he First Amendment guarantees freedom of speech and freedom of the press. Costly and time-consuming defamation litigation can threaten those essential freedoms. To preserve First Amendment freedoms and give reporters, commentators, bloggers, and tweeters (among others) the breathing room they need to pursue the truth, the Supreme Court has directed courts to expeditiously weed out unmeritorious defamation suits." Kahl v. Bureau of Nat'l Affairs, Inc., 856 F.3d 106, 109–10 (D.C. Cir.), cert. denied sub nom. Von Kahl v. Bureau of Nat. Affairs, Inc., 138 S. Ct. 366, 199 L. Ed. 2d 269 (2017). In Kahl, he rejected a defamation case by a prisoner who claimed that a press summary of his case falsely attributed a prosecutor's harsh statements to the sentencing judge. Kavanaugh applied speech-protective First Amendment doctrines familiar to defamation lawyers and found that the prisoner had not offered any evidence that the publication acted with the requisite actual malice. Similarly, in Abbas v. Foreign Policy Grp., LLC, 783 F.3d 1328, 1332 (D.C. Cir. 2015), he held that questions posed in an article could not be treated as assertions of fact, and therefore could not be defamatory. He again used fairly sweeping rhetoric about the application of the First Amendment to defamation cases.
But Abbas is controversial because Kavanaugh found that the District of Columbia's local anti-SLAPP statute did not apply in federal court. That ruling has made some people — including some colleagues and friends — fear that he's not sufficiently protective of free speech. They are, with respect, wrong. State anti-SLAPP statutes provide a procedural vehicle for defendants to get rid of meritless attacks on speech and recover attorney fees. Kavanaugh is clearly in favor of anti-SLAPP statutes in concept — in Abbashe acknowledges their purpose and importance. His ruling that state (or, in this case, District) anti-SLAPP laws don't apply in federal court is based on a rather wonky and esoteric area of law — which state laws apply in federal courts when state-law claims are tried there? Put extremely broadly, substantive state laws apply, but procedural state laws do not. There have long been disputes over how to treat state anti-SLAPP laws under this analysis, because they have both substantive and procedural elements. Other smart judges — including ones quite protective of the First Amendment — agree with Kavanaugh on this. I like anti-SLAPP laws very much, and from a result-oriented perspective I like to see them apply in federal court, but Kavanaugh's take here is not extreme and has to be viewed in the context of his strong defense of First Amendment rights in defamation cases. We need a federal anti-SLAPP law.
Conclusion. In conclusion, Kavanaugh's work on the D.C. Circuit show a judge strongly protective of free speech rights, and part of the trend of applying free speech doctrines both to classic scenarios and to government regulation. His stance on telecommunications and elections laws will get him painted as part of the "weaponize free speech" movement by results-oriented thinkers. He's strong on First Amendment limits on defamation law and his approach to anti-SLAPP statutes do not, as some have suggested, signal that he wants to make defamation cases easier. But though he might help upset applecarts by applying the First Amendment to regulatory schemes, and will not uphold broad speech restrictions, he will likely not overturn doctrines that make it hard for individuals to recover for speech violations.
UPDATE: I originally just linked to the original post, but then got Ken's permission to simply quote his entire post.