It's for the lights.
Like I said, ds1 has to wear make up on stage as well.
At three or four, they are quite old enough to be introduced to the idea of make up as something you do to perform. (I have to say at three or four they usually just stand on the stage and blink out at the lights anyway - it's really interesting to see the progression as they move through the dance school - and by ten or eleven, you can start to have really interesting discussions with them about the use of performance.)
All this hysteria bout stage make up is very funny.
I have lots of friends with three year olds in ballet who are all good right on fems and recoil in horror at their three year old having to wear Lippie. Most of them, if they refuse, get the photos back later, or come back after the show, and confess that they get it. Stage lighting is kinda harsh, and there's a reason actors have been wearing makeup under those lights for a heck of a time.
That in itself is a useful interest point for older kids - that parallel with a specific culture, and whether it translates to rl.
As I said, with older girls, who have been wearing stage make up for performance for many years, they see it as entirely related to performance. Entirely.
Sure, it takes a while for them to mature from that innocent three yo who wants to play dress up and be 'pretty' on the stage (hey, at three they are far more socially conditioned than a 12 yo who recognises the trope for what it is) but to run for the hills assuming this is somehow damaging her for life is somewhat unnecessary.
(I've been there, believe me. But now that my girls are well past the pink princess stage, I know that the make up has actually been a really positive introduction to why women in rl wear it - to perform. And that's an understanding they wouldn't have grasped from not being allowed it to wear it, at all, ever, and been steered to the pool)
Of course, as a parent, you are going to provide a backdrop to this. If the dd is surrounded by adults who ooooh and aaaaah when she's in her slap, and tell her how gorgeous she is, that will have an effect. If she is surrounded by adults who explain about the lighting, and the necessity to highlight facial features for the stage, and compliment her on her dancing, that will have an entirely different one.
I have never yet heard a dance teacher tell a group that their makeup was great. I've heard plenty comment on how the dance went.
All you mums of three yos in dance doing the recoil in horror thing might well end up with a feminist dd like mine. Who still wears stage make up. And sees it as an entirely functional thing. And wears none at all in rl.
Or you could forbid makeup until they are much much older, by which time they will have associated it as something that adult women do. Not something functional, for a specific reason.
So much trying to be a good fem. and so much handwringing.
Give it ten more years.
(maybe a couple more for the op)
Three is quite the worst time for delusions of gender.
and quite the worst time for feminist mothering. Boogie men (and make up) round every corner.