"Judges Propose Making Disclosure of Their Personal Details a Crime"

This would include group membership, information about where a spouse works, and more.

Josh Gerstein (Politico) has the story, with a link to the Judicial Conference of the United States letter laying out the request, including (bullets added):

2. PROTECTION OF PERSONALLY IDENTIFIABLE INFORMATION of judicial officers and their immediate family members, to include but not be limited to

• the primary home address;
• date of birth;
• social security number;
• driver's license number;
• voter registration information that includes a home address;
• bank account and credit or debit card information;
• property tax records and any property ownership records, including a secondary residence and any investment property;
• birth and marriage records;
• marital status;
• personal email addresses;
• home or mobile phone number;
• vehicle registration information;
• family member's employer, daycare, or school;
• personal photographs or photographs of a judicial officer's home;
• religious, organization, club, or association memberships; identification of children under the age of 18;
• and any other unique biometric data or piece of information that can be used to identify an individual….

4. MANDATORY REMOVAL OR REDACTION OF JPII UPON WRITTEN REQUEST
SERVED ON ANY PERSON, BUSINESS, ASSOCIATION, OR AGENCY. Upon written request, a person, business, association or agency must, within 48-72 hours of receipt of the request, redact from the public record any existing JPII and may not thereafter knowingly post, display, sell, share, trade or transfer JPII, including publicly accessible and displayed content. No person, business or association shall solicit JPII with intent to do harm to a judicial officer or immediate family member. The written request by a judicial officer, or his or her representative, to remove and/or to redact from the public record JPII of the judicial officer or an immediate family member shall not require a showing of fear of harm or immediate threat and shall remain effective until revocation of the request by the judicial officer or a surviving immediate family member.

Other sections focus on removal of information from the government's own publicly accessible records, so this seems focused on private entities, and seems to use "the public record" in the sense of "publicly posted information" rather than government records (which wouldn't generally be under the control of a "business" or "association"). If implemented as requested, this would require newspapers, blogs, and other publishers to, for instance:

1. Remove articles discussing a judge's membership in some controversial group, or a group that is connected to litigation pending before the judge.
2. Remove articles discussing how the work or schooling of a judge's family member's might create a possible conflict of interest or source of bias.
3. If a judge's child has been accused of crime or misconduct (in school or athletics or otherwise) by name, remove articles discussing this in connection with the judge (e.g., if some people think the family connection may have led to a sweetheart deal).
4. Remove articles or posted court documents discussing lawsuits related to property the judge owns (or recusal motions based on the judge's property ownership) if those articles or documents contain property tax records or address information or home photographs.
5. Remove videos or up-to-date photos of a judge involved in some event or altercation, since those would be "biometric data or piece of information that can be used to identify an individual."
6. Remove videos or photos of a judge's family member who was involved in some event or altercation, if "an individual" is read to include family members and not just the judges themselves.

This strikes me as unconstitutional, even recognizing the serious threats that federal judges sometimes face, from disgruntled litigants and others.

The case for restricting the publication of home addresses is stronger than for some of the other items, but even such addresses are sometimes matters of public concern, as item 4 above suggests.

Moreover, rightly or wrongly, in most of the country residential picketing is legal; and the Court has strongly suggested that, while content-neutral bans on targeted residential picketing are constitutional, they are constitutional because they still allow "[g]eneral marching through residential neighborhoods, or even walking a route in front of an entire block of houses." It's impossible to organize such constitutionally protected events without informing people of the address of the person who is being criticized. Perhaps because of this, courts have generally struck down bans on the publication of government officials' home addresses, see Publius v. Boyer-Vine (C.D. Cal. 2017) and the cases it cites. (Disclosure: I was one of the lawyers for plaintiff in that case.)

(The case for restricting the publication of certain information that seems to have very little likely value other than to facilitate crimes—often financial rather than physical—such as social security numbers, bank account numbers, and the like might be quite strong; see pp. 1146-49 of my Crime-Facilitating Speech article.)

Naturally, before judges are judges, they are people. One can't ignore that this issue literally hits federal judges where they live, and the fact that the letter comes from the Judicial Conference, with Chief Justice Roberts' letter on the letterhead. Still, I hope that Congress or (if the broad version of the law is passed) the federal courts will recognize that the proposal is too broad.