In a few ways.
1. A very likely scenario is that a group posts the address of a researcher on its website, urging people to come out and protest (which, although quite controversial, is still legal and protected activity). Prosecutors may say this “incites” illegal activity, or a researcher may say they are fearful of the picketers. As a result, the group wouldn’t be able to spread information about their activities and spread their views. The Internet is critical for grassroots organizing, and lawmakers clearly know this and are attacking this.
2. There’s another type of threat posed to free speech activity, and that’s the chilling effect of legislation like this. The “eco-terrorism” rhetoric, combined with vague, overly broad legislation, and harsh penalties, is intended to make people afraid to use their First Amendment rights.
Best, Will