Holding yourself just outside a large, powerful, controversial social alignment is a pretty uncomfortable thing to do; people in the ingroup aren't going to think of you as an ally, they're going to think of you as a heretic. And thanks to outgroup homogenity, you're going to find it very hard to distinguish yourself from X from the perspective of people outside it. (Insert your own examples here; I'd add some, but all the ones I can think of are politically sensitive.)

If you're loud enough and can get enough people on board early, you might be able to establish yourself as a sustainable group mutually distinguished from X. But I don't think it's possible to reliably keep the groups straight as far as people outside them are concerned: once you've defined your ideology you can't pick and choose the criteria people will be using to make those judgments, so they'll correctly note the similarities more often than not.