What if they say they've felt like a cat for as long as they can remember?
Look, there's a nuance here that is nearly always swept under the rug and ignored. I'm going to try to explain it.
I have always felt taller than I actually am. Genuinely - I'm not making this up for illustrative purposes. My mental image of myself is realistically about 5'8". I feel like I'm at eye level with my boss. I feel like I'm only a small bit shorter then my 6'2" spouse. I've always felt taller. I'm 51, and I still end up slightly surprised when I can't reach things on the top shelf at the grocery store. Logically, I know that I'm 5'1", and I know that I've always been short relative to my same-age peers.
I've had several discussions with my spouse and my family and friends about this. They believe me when I say I feel taller than I am. They don't think I'm making it up. They believe that I feel this thing, but they don't believe the thing itself. I'm not taller than I am, I'm not eye-level with my boss, I'm not near-in-height to my spouse, and I can't reach the top shelf at the grocery store. That's objectively true, it's factual. My feelings about it are irrelevant, and the sincerity of my feelings has no bearing on reality for myself or for anyone else around me.
Whether you or I or anybody else believes a male who says they've always felt like a female for as long as they remember doesn't matter. Their feelings about it don't actually matter, nor does our evaluation of whether they're sincere about their feelings. The factual reality is that they're male. They might feel like they're the opposite sex, but they are not the opposite sex.
I can believe that a schizophrenic genuinely and sincerely feels that aliens are whispering the secrets of the universe to them. They can sincerely believe it, and I can acknowledge that their belief seems sincere to me. But that does not in any fashion mean that aliens are actually whispering to them. And it definitely doesn't suggest that I should pretend that the aliens are real, or that I should accommodate their false belief and false feelings.
That's what a delusion is - it's a false belief. A hallucination is a false perception. In this context, saying that a male with a transgender identity is delusional isn't a moral judgement - it's a statement that their belief is false. They are NOT the opposite sex. The genuineness of their feelings is irrelevant to that. They were not born in the wrong body, that's impossible.