While even Republican Donald Trump seems happy to throw away the Second Amendment for people the government declares suspicious, but not like "we think they committed a crime we should arrest them for" specifically, for uncheckable reasons, Libertarian Gary Johnson stands (as things now stand) strong.
His campaign told Daily Caller in a written statement from Joe Hunter, Johnson's communications director, that "Gov. Johnson believes Second Amendment rights are too fundamental to be denied without due process, and being put on a list arbitrarily by the government is certainly not due process."
The campaign also:
pointed TheDC to a recent blog post by the ACLU titled, "Until the No Fly List is Fixed, It Shouldn't Be Used To Restrict People's Freedoms." The ACLU is currently in a legal challenge against the no fly list. They say it is "unconstitutionally vague, and innocent people are blacklisted without a fair process to correct government error."
When Johnson was given the chance to think out loud about the issue at length with Fox News' Stuart Varney, he sounded less dedicated to the hardcore principle of the thing. He said "we should be open in principle to discussion" about how to keep guns out of certain people's hands—he picked the mentally ill, not people on "terror watch lists," as his example—while granting no actual proposal he's ever heard would, he thinks, actually do just that without capturing the innocent in the dragnet as well, depriving them of rights for no justified reason.
When Varney said he was surprised he didn't hear just a full-throated "the Second Amendment is what it is, no restrictions at all" argument Johnson fell back on noting, well, there are "varying degrees of libertarians" but that you could "count on me to have a process to look at these issues." Many libertarians would doubtless have wanted a "you can't just give government power to put non-criminals on a list that denies them of a right, full stop" answer, but that's not Johnson's style.
He did say to Varney that he didn't want to answer a theoretical question about a list that really did contain nothing but actual terror threats. Johnson said such lists don't exist, so there is no point wondering about them. He stresses the false positives and errors in such lists as the problem with relying on them to deprive those who have never been arrested or convicted of their Second Amendment rights.
Johnson on Fox:
Johnson spoke to me the other day about why he doesn't think restrictions on gun access in general are a smart response to crimes like Orlando, and that in fact more guns might make such situations safer.