Actually this isn't true. Or, at least, it wasn't true. There used to be a pretty well established "immigration procedure," that included time spent "living as a woman" (aka: social transition, one or two years I believe), a medical diagnosis of gender dysphoria, counselling that wasn't conflated with conversion therapy, and only then, cross sex hormones and legal recognition of your new sex.
Trans people (then referring specifically to transsexuals) went through this procedure, regret was pretty much unheard of, and there was next to zero pushback about trans inclusion in society. "TERF"s, back then, were a tiny fringe group who pretty much everybody agreed was nasty, bigoted and transphobic.
Fast forward to 2022, and trans lobby groups have pretty effectively erased all of these common sense standards. Insisting that all we need to do to tell if a male is a woman on a particular day is ask him. Suddenly, everybody who doesn't embrace this quasi-religious belief is a "TERF."
Now, consider immigration in the traditional sense. What do you think would happen in the US if it became possible to simply "identify" as American? If at passport control, all our hypothetical Somalian-born person had to do is say they "felt" like an American, and they instantly gained all of the rights and privileges of any American citizen? Would the people who asked if this was a good idea be anti-immigration? Or racist? If somebody known to have committed terrorist acts against American was granted citizenship under these new rules, would it be bigoted to object?