they might have been selectively collecting them, if not engaging in worse fraud.

Sure. So might anyone quoting anyone about anything. What would fraud look like here? It would mean that actually there are a bunch of cases of sexual assault by trans people, or people pretending to be trans, in public restrooms. It shouldn't be too hard to find some, if so. Please feel free, and I will of course update my opinions in response to whatever you find.

these policies have been in place for less than two years

The first few days listed in the article itself: 2008 in Colorado; 2011 in Connecticut; 2007 in Iowa; 2005 in Maine; 1997 in Massachusetts.

left-wingers are notorious for creating policies with glaring perverse incentives [...] that almost no one avoids getting a job so as not to lose welfare benefits [...]

Well, as it happens, the only example personally known to me at present of someone who contemplated getting a job and changed their mind because of the impact on benefits did so because of changes to the tax and benefit structure introduced by a right-wing government, and the incentives were much better aligned before that government made the change.

Of course one anecdote isn't much evidence for anything. The general point here is that it's by no means only left-wing governments that create policies with perverse incentives. (Famous examples: "Abstinence-only" sex ed in schools doesn't stop kids having sex, but it does make them more likely to get pregnant when they do. Restricting the availability of contraception increases the incidence of abortion and single-parent families, both of which the opponents of contraception usually say they're more strongly opposed to.)

In any case, what exactly is your argument here? It surely can't be "Allowing trans people to use public restrooms corresponding to their new gender is a policy brought in by left-wingers; policies brought in by left-wingers often have perverse incentives and do harm; therefore this policy has perverse incentives and if you think it won't do harm then you're wrong", but what is it?

OK, so also give the striped lion a collar saying "I'm a tiger".

Let's continue that discussion when you're prepared to engage seriously with what I'm saying. (If you genuinely can't see highly relevant differences, let me know and I'll point some out.)

the structure of my brain and my personality, behaviours etc., are in male rather than female cluster.

OK. So if a trans person's brain structure, personality, behaviours, etc., were found to be nearer typical-female than typical-male, would you then consider them something other than deluded/hallucinating/bullshitting? What sort of differences in brain structure would be most relevant? (Brain structure is kinda hard to explore, beyond the very coarsest features; what if we couldn't tell about brain structure but their personality and behaviours were "more female than male"?)