I think the poster has a legitimate point. As an end user you can protect yourself, but as an organization that cares about Internet freedom it's a legitimate concern to consider: "Are we enabling tracking through the use of our advocacy, and if so can we avoid that."

Although, I wouldn't go so far as to say that I can't take them seriously because they decided to use the buttons.

And this is why movements fail, because everyone wants to add their own agenda.

Don't get me wrong, I'm not saying that privacy is not a worthwhile concern, but this movement seems to be about protecting the Internet from government abuse, not about privacy practices of private companies. Sure, it could be about both, but that would dilute the message and create a handicap, especially if it means having to avoid some of the primary methods of communication online.

I think this organization has bigger issues than facebook buttons on its website

Not really. If Facebook already established a cookie in your browser they will still receive it in all browsers but FF.