Religion, which I already mentioned and you completely hid from. “Hispanic” is also purely a matter of self-identification on all government forms right now (and is typically a separate category than race), and it’s doubtful they’ll come up with some kind of hispanic-test for it.
If he just fills out ‘f’ on a form but doesn’t actually ask people in his day to day life to refer to him as female, he’s scamming, and it’s so abundantly obvious that there’s no real need for discussion. If she actually spends her day to day life consistently insisting that people refer to her as ‘she’ and otherwise interacting with people as a woman outside of the single form for the program, then I don’t see what remedy is needed. She’s going to not be accepted by her conservative friends since they’ll consider her a freaky ‘man in a dress’, but if she’s doing it as a scam is also not going to be accepted by liberals because she’s hurting actual trans people. Whatever one-time bonus she gets from the program is going to pale in comparison to the costs of actually trying to live life that way.
BTW, you (and other people arguing your side) would look a LOT less bigoted if you got some basic education on what life for a trans person is like. It’s not walking down the street and having people hand you affirmative action cash and jobs, it’s constantly being vigilant for threats of physical violence, losing jobs or being turned down for jobs because of your identity, taking your life into your hands if you’re on a road trip and have to pull over to a gas station to pee, and a lot of other unfun stuff.