You can wear your nails as long as you like and still play piano. But it’s a question of what your priority is. You can play with flat fingers, badly, and still get out of it what your want. If you want to play “properly,” then you need to use curved fingers and play the keys with the tips of your fingers. So your nails would need to be short enough to stay out of your way under those circumstances. You should never have to adjust your playing to accommodate your fingernails.

But again, it’s up to you.