I noticed a strategy that many people seem to use; for lack of a better name, I will call it "updating the applause lights". This is how it works:

You have something that you like and it is part of your identity. Let's say that you are a Green. You are proud that Greens are everything good, noble, and true; unlike those stupid evil Blues.

Gradually you discover that the sky is blue. First you deny it, but at some moment you can't resist the overwhelming evidence. But at that moment of history, there are many Green beliefs, and the belief that the sky is green is only one of them, although historically the central one. So you downplay it and say: "All Green beliefs are true, but some of them are meant metaphorically, not literally, such as the belief that the sky is green. This means that we are right, and the Blues are wrong; just as we always said."

Someone asks: "But didn't Greens say the sky is green? Because that seems false to me." And you say: "No, that's a strawman! You obviously don't understand Greens, you are full of prejudice. You should be ashamed of yourself." The someone gives an example of a Green that literally believed the sky is green. You say: "Okay, but this person is not a real Green. It's a very extreme person." Or if you can't deny it, you say: "Yes, even withing the Green movement, some people may be confused and misunderstand our beliefs, also our beliefs have evolved during time, but trust me that being Green is not about believing that the sky is literally green." And in some sense, you are right. (And the Blues are wrong. As it has always been.)

To be specific, I have several examples in my mind; religion is just one of them; probably any political or philosophical opinion that had to be updated significantly and needs to deny its original version.