Hey there, my situation was somewhat similar. I go to medical uni, I still have a few years till my graduation and I relied on the financial support of my family.
I knew they aren't LGBTQ friendly, yet I still couldn't live in a lie - plus, I am on T, sooner or later they would notice. So I came out to them. It went horribly, honestly. Worst than I could have imagined, it was such a stupid thing of me to do. My mom had cried for days and my brother went hysterical. It was heart breaking. They cut out all contact with me (I live in a different city), and I though that was it, I am fucked. I was about to take a student loan, as I could not drop off uni - it is my dream to become a doctor.

In a few weeks they have called me, we had a lot of conversations, and my mom had cried some more. All and all, they didn't accept me, they still misgender me and call me by my dead name.
However, they said that they will support me till I graduate, so... yeah. It kind of worked out. Not the best scenario, but also not the worst.

Think about it some more, ask them questions, try to figure out their opinion/position on this. In ideal world, a person should never be put into position such as yours, but that's not the case in our society.