I don't really find that ideology is anywhere near as sticky, as I've had a much easier time discussing nuances with ideologues compared to religious people, and, more importantly, ideology is just nowhere near as
stand out.
You can be a communist without anyone knowing. I have a set of some very odd beliefs, nobody really knows unless they ask.
You can't quite do that with religion when you have days you can't eat meat or you can't work because you have to go to a special building or what not. Or often religion instructs you to talk about it. Ideology can stay in your head; religions (properly followed) tend to be disruptive to one's entire lifestyle, so if a society doesn't protect it, it can as well declare the religion invalid for what that's going to do to it.
Which might be what the society wants to do, but you should understand what it is that you're doing.