I apply the eyeliner first. Then curl my lashes, followed by applying mascara.
If the eyelash curler wipes off you eyeliner, you can change two things. One, get a better liner. I use liquid liner, specifically Stila waterproof all-day liner in black. Stays like magic, no wearing out or anything even if I get sweaty and such. Two, don't bring the curler too low on your lashes. Aim to get it and the curl more in the middle versus starting right at your lashline.
I do eyeliner before mascara because I find some times if I do eyeliner afterwards and my eyes start to water from doing it then my mascara smudges off and it's just not fun, I also curl my lashes after mascara and I KNOW it's bad to do that but I've been doing that for 5 years now and I haven't lost any lashes from it thankfully lol, it's a bad makeup habit I have.