Sure they do, Essorant. At a minimum, they give hope and a sense of belonging and purpose to folks who might otherwise feel unnecessarily discouraged. It's a perfectly understandable and fine thing to do.
I don't agree with the petition, but my agreement isn't necessary for those who sign to feel renewed hope and energy. It's part of the play of political dialogue. I don't think it's uniquely American, even. You get the same thing in Canada around loads of issues, even fiery issues. It helps to keep the talk going, and it helps keep the conversation below the level of physical action. It's very useful.
While I don't agree, These folks have a point and the right and need to make it, the more plainly and clearly the better. As of course, do we who tend to disagree, though that's for a different place and time.