Should academics be concerned about professorwatchlist.org There is a relatively new website: http://professorwatchlist.org/ whose mission:

is to expose and document college professors who discriminate against conservative students and advance leftist propaganda in the classroom.
Help us identify, and expose more professors who have demonstrated liberal bias in the classroom.

What are the likely consequences for a US academic that is exposed as having a liberal bias in the classroom?
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.