[[ Mmm, I’d say this one is partly up to personal interpretation. 

But let me list some things and you can take away what you want from it–?

As for my answer, I really have two opinions on this? On the one hand, I believe they do grow facial hair but like East Asian men (as they seem to heavily resemble/be modeled after), the hair is really thin, doesn’t grow fast, and can be shaved off with ease. 

Then I just think no they can’t because Kishi didn’t want to have to deal with it and wouldn’t think facial hair would add any quality to their appearance/doesn’t need to show age via facial hair, so it’s just because he didn’t feel like it. 

So one in-universe reason and one out-of-universe design reason.

As for the other stuff– there are lots of men in Naruto with facial hair. Some didn’t start out with it and some have it in later designs (Chojuro and Kiba and Shikamaru as just three examples of facial hair in later designs). 

Some have it because it shows a certain type of character design (A, Darui, Ohnoki), etc. 

I’ve seen background Uchiha in the  manga panels with facial hair, so in-universe it’s perfectly possible Uchiha can grow facial hair, I just don’t try to think on it too deep because it’s likely mainly a design thing. Even Fugaku didn’t have facial hair. 

If you want to see really nice art of Uchiha with facial hair, I’d recommend @renamon15, their art is really nice :3 ]]