Once upon a time, I marched through San Francisco to support... hmmm, I forget what it was exactly I was supporting. I think it was "Reproductive Rights."
That was the first, and last, time I ever marched in support of some political cause. The march was overrun (in my opinion) by people with signs supporting other, unrelated political issues. "Workers Unite: Unionize Now!" and "Join the Socialist Party of North America!" and "It's Potato, Stupid!" (this was back in the Dan Quayle era) and "Bikers against Helmet Laws" and on and on and on.
I didn't want to be associated with all those wacky causes. So I didn't bother going to any more political marches; I wasn't going to implicitly support a bunch of stuff I didn't agree with.
So I agree with the position of the Amherst 4'th of July parade organizers. Anybody can march in the parade, as long as they don't try to inject whatever wacky (or extremely important, depending on your point of view) causes they care about into the event.
Oh, and a footnote for the parade organizers: Less candy, please! How long has the "tradition" of throwing candy at kids been going on? Paraphrasing (badly) JFK: "Ask not what the parade can give to you, ask what you can give to the parade...."