You theoretically could be fined 250,000 dollars and go to prison for 5 years if you don't register. I don't know of this happening to anyone but it's probably better not to do have the "dirt" on you. Even if the situations where it could be used against you aren't that likely they are still possible, so you might as well register.
If you don't do it before you are 26 you will be denied student loans, federal job training, and any federal jobs. Again, even if you don't think you will do these things it is better to have them as an option. If you are not a citizen or give up your citizenship for any reason you will not be able to gain US citizenship.
Plus, think about it seriously... if you don't register, is that really going to stop the government from finding you if there is a draft? Probably not, it will only slow them down a little. Also they obviously do not have a great track record towards trans women so don't expect any legal sympathy there although it might be enough to disqualify you for mental health issues if they ever start up a draft.

If you are that worried about it, the best thing is probably to figure out an "escape plan" in the case of a draft. The most likely thing to work would be to leave the US for an anti-US country (socialist countries like cuba or venezuela come to mind and vietnam even has a citizenship provision for people who are forced to flee their countries for "defending socialism", iran, etc, maybe even Russia or China), but this would require to speak the language and could still be tenuous. Canada is traditional but they extradite and/or prosecute defectors sometimes, so they are not necessarily very safe.
A smaller country politically neutral would be risky because it would be more susceptible to the machinations of larger countries. The UK basically just extradites everyone to the US although if Scotland ever leaves they might be sympathetic to defectors. But basically this means that there aren't a lot of english speaking countries available. However, if you have a college degree you could probably get a job teaching english in many countries. This would give you more time to learn the language since foreigners are usually hired to teach english
in english.
Now people here are going to think I'm nutty becuase I've obviously thought about it a lot, but at least I'm prepared.

The draft has happened before. Even though it's hard to imagine the political climate shifting enough for it to happen it still does not hurt to have plans for how you would respond to various situations. The hardest things to deal with are the ones you haven't prepared for.