I don’t think it’s a problem, and it’s such a gorgeous combo!
Rae / [name_u]Ray[/name_u] is a very common middle name. I think people chose it because it’s a nice, simple middle name for their little girls. It reminds me of [name_u]Marie[/name_u], [name_f]Ann[/name_f], [name_f]Mae[/name_f], [name_f]May[/name_f], [name_f]Rose[/name_f], [name_f]Dawn[/name_f], etc, etc.
I’d never even think to look up the meaning of [name_u]Rae[/name_u].
I also wouldn’t know the meaning of [name_f]Tabitha[/name_f], if it wasn’t on my list! I love [name_f]Tabitha[/name_f] with the nn [name_f]Tabby[/name_f] (and I’m a cat lover). People who’ve never looked up the meaning would never guess it means gazelle.
If it really bothers you, then it can be worth rethinking. But if you’re worried about other people making the connection, then I say not to worry and go for it!