Should academics be concerned about professorwatchlist.org

If that website is really about what it says it's about, then I don't think there's anything to worry about. Academics should be open to criticism, especially if they are vocal about their political opinions. Academic freedom means the government should not interfere with what professors teach, not that they should be shielded from criticism. There certainly is political bias among university professors and it's not unhealthy per se to question that via independent media.

Off course, this website is very partial and lumps together extremists, people under FBI scrutiny or who were convicted with people with simply non-conservative opinions, and people whose research actually contradicts some of the American conservative positions. That last bit is probably the only worrisome aspect.

I suspect readers of that website are really looking for a confirmation of opinions they already have. I don't think it's going to have a lot of traffic from random people (apart from the one you're generating with that link). That is also true of blogs and website from the other side of the political spectrum.

If such websites challenge facts because they conflict with their political opinions, then there is a threat and it's our job to fight it with science, not with political activism.

I very much doubt we need to be concerned with it at this point.

Collections like this have existed for a long time. When I was an undergrad, a minor incident on campus got spun up into Clear Evidence of Oppression (tm) and gets trotted out now, more than a decade and a half later. The site is, at the moment, pretty poorly designed, primarily a collection of innuendo and "X professor was mean to me", and like many user-submission dependent sites, is currently somewhat inundated with obviously fake examples.

Beyond that, the very pretense of the site, that there's a clear bias in favor of professors pushing liberal ideas that pervades and dominates academia also implies that exposure of a professor doing just that...won't do much, because an academics career is primarily dictated by other academics.

The list is only a threat given moves to shift the evaluation of academics into the political sphere. But those are separate actions, that should (or should not) be opposed on their own merit, because they have implications far beyond a random PAC's website.