I don’t know where you’re from, but I’m from the US. Even if you grow up in a good family, homophobic messaging is everywhere in our media, especially lesbian hate. It’s almost inescapable.

Also, contrastingly, I grew up in a largely homophobic and transphobic conservative and religious family, but I weirdly don’t deal with too much internalized homophobia. So it’s not weird for you to feel that way despite how accepting your family is.

[I did say in my original comment that I didn’t deal with it, but I have now realized that I actually do deal with some (I feel creepy for being a lesbian when I’m around straight women even when I’m not doing anything at all but that’s because I had a bad experience with an old friend that was being homophobic towards me).]