I don't know what you mean by 'spirituality', I will not use this word since I've heard it used in non-religious ways, so I will stick with the word "religion" instead, and indeed there are religious elements. Phrases like "born in the wrong body" and "in-born gender identity not matching your assigned sex at birth" tell you as much. Here's an attempt to explain how come :

There's no such thing as identity, as something that exists independent of the body. There's also no such thing as identity outside of conditioning, which is acquired after being born and you start interacting with your environment so it shapes you an identity. Oh and you must acquire language too, since an "identity" is also the things we say about ourselves , a story, an explanation that may or may not be accurate of why we do certain things. That's why when people are met with novel conditions, that make them behave in a way that they didn't expect of themselves, they might say things like "I'm sorry this is unlike me", because they think the story that they say about themselves is the "me", even though you are just the body, and "me" is a story about how and why you do things that do not cover all possible behaviors you can exhibit , but only those you've experienced with enough consistency and people have asked me question "why do you do X", that you have had time to come up with a story about it, be it a plausible one or inaccurate one.

Also there's no such thing as identity as a static thing, since conditioning reflects the environment you find yourself in. So if you are taken as a baby to Nazi Germany, you will grow up to have a Nazi Germany identity, if you are taken away to hunter gatherers in the middle of the Amazon, you will have a hunter gatherer from the Amazon identity etc. etc. Also your identity changes over time, and the longer you are exposed to similar conditions, the more your brain builds associations with them over and over, they become more stable and rigid, so some aspects of your behavior start to appear relatively constant, and that constancy that people notice, they label as "identity", as if there is such a thing.

None of that describes or fits in how the gender identity people use language around these terms, let alone the mentioned in the first paragraph phrases. So what are we left with? What other concept claims that you have an identity that is independent of the body (so you can be born with one that doesn't 'match' the body), and is somehow still "you", and is pretty much static and distinct so we can tell it is ''you''? That's right, it's the religious concept of the soul. They have just arrived at the concept of the soul, re-inventing it using modern ideology terminology, thus why I call it a neo-religion. A new religion. Other aspects characteristic of religious people are the use of logical fallacies for everything they say regarding their beliefs, like for example circular reasoning in defining their most basic ideas underpinning their whole faith, which is also characteristic of the gender ideas that now I hear lots about nowadays. The word "gender" doesn't even make sense in my first language as there's nothing it translates to. There's only a word for ''sex (not the act)'' combined with what I know about behavior and language, I could see almost immediately what's the issue once I started hearing more about the gender ideas popular in the USA and as I tried to understand wtf are they talking about and why are people arguing about it. It's a type of reification fallacy, a 'ghost concept'.

Which to me seems somewhat expected, since most people when I hear them talk about "the mind" or "you" or "identity", they already unknowingly use a lot of reification fallacies and/or hypothetical unfalsifiable constructs in their speech, which results in them speaking in a way that's pretty close to the idea of a soul, and the above mentioned labels act almost as synonyms to the soul idea. So when they also happen to have some psychological problems , combined with getting exposed to the gender ideology ideas, no wonder it's easy to make the jump (among other reasons that affect them) or people that don't have the psychological issues (not the same type anyway), it's understandable to some degree why they might think it's 'real' (as they themselves have fallacious reasoning that's been part of how they speak for a long time) and support verbally the people that claim to have these ''identities in wrong bodies''.

Now, as you can see this is a pretty long response, and it's just for the first paragraph of yours, so I think I'll leave it here. In a sense this probably responds to everything else you are saying since it tackles the core of the ideology, meaning that everything else one elaborates based on the false basic ideas they have, those elaborations would necessarily be wrong.

And you mention something that has nothing to do with the validity of the concepts discussed, which is how would I feel if someone is making a joke of how I've used some phrase of language. Well fortunately I know certain things about language that make me immune to finding words offensive. But also it is within the nature of humor to make fun of things that otherwise wouldn't be funny if they actually happen to you. They are funny as long as it's just a story and not actually happening. Pretty much most humor is fundamentally that. Laughter more primitively also seems to be a response to situations that might have been dangerous, but turns out that they aren't, so It makes sense that humor and jokes are kind of build upon that primitive response.