How is religion any more or less immutable from political beliefs? In my view both are fully equivalent.

Religion is a protected class to stop zealots from waging wars on each other, got to nip it in the bud before tension builds up. It is a very rational reason even if the protection shouldn't be needed in theory.

In some cases (e.g. Jews, Amish) the lines between race/religion/national origin become pretty blurry. I agree that it's the most ambiguous of the classes, though.

Personal traits are always mutable. What seems (and may be) immutable to you could be mutable to others.

It's technically true that you could find some way to dye your skin a different colour, but I don't think most people would find that to be a realistic solution to anything.