If you are going to a private school, it's kinda implied money isn't a huge issue anyways. Your parents are paying for you to attend this exclusive school, after all.
But you can't take Johnson Academy's uniform to Brentwood. So, if Brentwood isn't having a sale, what then?
My son came out to me a little at a time. Testing the water saying they are lesbian, before they came out as trans. He came out to me in a letter, and was also scared of rejection.
I knew the statistics, that LGBTQ+ kids have a higher rate of self-harm, depression, and suicide. Knowing nothing at the time, I accepted him on the spot, every time. There was a small pushback from the wife, but I pulled her to the side in private, laid it out, and said he needs our support, regardless of weather we understand anything.
Your parents sound like they are good people, and your mom is letting you know she is at least okay if you were gay.
Don't take this as word of God, but it sounds to me that she may not initially understand you, but she will try. It's how I was, and now my kids father is their mother lol!
As a parent, watching my kids grow, and seeing their struggles with coming out and anxiety, seeing how MY family has treated them, and me, I can only grasp at how you are feeling now. I know it's gotta be tough.
I wish you the best of luck, whatever you decide.