Religion is not part of your identity, it's at best an opinion that you are (potentially temporary) holding now.
And this is wrong for CoCs to include religions, or political views, on the same level as identity defining traits like gender and race.
And that may be one of the big cultural difference between the US and my country.
Here the generally shared idea is that people are citizens of the republic first, before anything else. Such a comment from a politician would elicit a terrible uproar.
That being said, anything can be part of your identity, you can define yourself as punk rock if you want. What I mean and thought you understood is the difference between what is intrinsically you and not. Yes of course, to many, religion is important like veganism can be. But it remain a mere choice to keep it that way.
Apostasy is always a possibility and that makes it different in a way that equating both kinds of identities is lessening the damages one sustains when attacked on a fundamental part of its person-hood. If your race is criticized, that's an attack on your humanity. If someone criticize your belief system : meh none is challenged otherwise than on a thought level.
Is gender on the same level as race though?
You can't change your race but you can change your gender - both in cases it's warranted (gender dysphoria) and in those it's not (otherwise).
Also it's disingenuous that you say religion is not a part of a person's identity, when in fact there are people to whom it's an important part of their identity as a person. Sure you can argue relision is a choice - and I can grant you that - but then it's the same with non-gender-dysphoric transpeople;they just chose a different gender than their biological sex for an arbitrary reason.
As spiritual being maybe but not as human being, that is technically wrong. Your race is intrinsically you and being derogatory to it is lessening you as a fellow human.
Since that even in the most fundamentalist country, the most devout person has technically the possibility to personally wake up and change his mind (apostasy), religion is fundamentally an other, lesser kind of identity. As being vegan.
Giving religions more respect than they deserve is wrong and extremely dangerous. See Salman Rushdy and Charly Hebdo to see what this kind of thinking leads to.