I think it depends on where you live. Changing gender marker can vary wildly from state to state, country to country. I've read here some countries require RLE for a year or two. Some US states you have to jump thru hoops while other states it is much easier.
When you do change your gender marker, that's just the start. You have school records, taxes, social security, credit bureaus, former employers, insurance, investments, banking etc to change.
I'd almost think it'd be easier to get approved for your loan...then change everything afterwards.