kieren,
Welcome to the site.
There have been many members here and many trans people who have experienced similar situations to yours. There is a section here called youth talk for mostly under 18s but I think you would find a lot of posts similar. It is common enough that trans folks of all ages with living parents have posted through the site.
There are a lot of ways to deal with this. One of them is to try to help them understand how you experience the world. Seeing from your perspective, sometimes changes other's opinions. If you could convince them to read it, there are is a lot of informational text to help others understand as well as open letters to parents.
There is even a video I saw lately that is about coming out, aimed at the family for terrified trans folk. There is more info than this, but here are some starters.
https://www.susans.org/wiki/Transsexualism_-_Information_for_the_familyhttps://www.susans.org/wiki/An_open_letter_to_parents_of_transsexual_childrenhttps://www.susans.org/wiki/An_open_letter_to_the_parents_of_transsexual_children_No._2Some people have been able to convince their parents it is not a terrible thing and no one has to be blamed or embarrassed. Others have had to move on, at least for a while. While it is painful I would ask that you not cut them off if this ends up being your course of action. Sometimes, they come around later.
I also want to share some links with you. They are mostly welcome information and the rules that govern the site. If you have not had a chance to look through them, please take a moment:
Things that you should read
Once again, welcome to Susan's. Look around, ask questions and join in. I wish you love, acceptance and a smooth path.
With warmth,
Joanna