I find it almost always makes more sense if you view that sort of "whacko PR" from fringe groups as being internal propaganda rather than designed to sway people to their side. The cognitive dissonance comes from the belief that PR is meant to expand your supporter base. It's not, it's meant to cement your control.
think about this: PETA would have an "elite" group of leaders who are in control, and want to stay in control. They could have an inclusive message that brings in a lot more supporters, but ultimately, the new supporters will be "moderates", and come to vastly outnumber the "elite". This could only really end with some of the moderates staging some sort of leadership coup and taking over the organization.
Imagine an analogy of a "club for geeks" which is really geeky, so you get a stint as president and get the idea to do PR to bring in more "average people" and it's really successful, so now the club is 10 times the size. However, at this point, the "average" non-geeky people have other ideas about how the club should be run so they effectively take it over, changing it's core mission statement. How would you feel as one of the original club members?
So, instead of that, the "elite" double-down on the rhetoric, which drives away more "moderate" supporters. This leaves a rump of die-hard ideological followers who are beholden to those core beliefs. The chaff - people who might question the current leaders - are brushed away.