I need to purge.
Not sure how old your girls are, but if I were you, I'd tell them they have 3 days to purge their extraneous junk or you'll throw it all out. Make-up has an expiration date, usually a year, so if you think it's been open for more than 12 mo, they need to throw it out for hygiene reasons.
Most women have stuff they've tried and haven't liked, but couldn't bring themselves to throw out, so be a little gracious. Just let them know the clutter is bugging you, give them the three days, then follow through if they don't purge on their own.
My 16 yo doesn't throw stuff out easily, so this is what we do and it works. Sometimes she'll do her own purges, and sometimes I do them.
The "girl stuff" in our house can be overwhelming too.
Why do you have to do ANYTHING with it?
If it's soaps, shower gels or the like & it was in the bathroom, I'd be using it myself.
I'm with Sabr - why throw it out?