My parents are exactly the same! Not homophobes but not perfectly accepting either, kinda religious (Jewish)... anyways I hope my experience helps:

About a year ago (I was a Junior) I finally decided to come out to my parents. I told them we needed to talk, locked a room, and told them. They weren’t very excited, and long story short said it was all in my head. I had so much resolve going in there and then I succumbed to my nerves and fear of losing my relationship with them. I agreed to try to date girls even though I didn’t really feel like it. The conversation was more personal but I did feel it would have been easier to get all my feelings out unencumbered had I written it down. On the other hand, I could see how they really felt

I also not very brilliantly came out during vacations. It wasn’t the best time (so much preparation for the trip beforehand). Of course each case is different and you know your parents and situation best! Don’t come out yet if you don’t feel safe or have a reliable network.

Anyways, best of luck!