It's very much a psychological thing with me. I stopped wearing make-up regularly by my mid-20s. When I started escorting I always wore lightish/natural make-up during the day, with a slightly more dramatic version for evenings. The first couple of bookings I did without did freak me out a bit, but I'm more relaxed about it now, and sometimes even suggest that I can be ready sooner without it - only one regular has ever said he'd prefer with. The two regs I do 15m quickies for know I won't get made up especially for them as they usually book quite (sometimes very) short notice.
As others have said, it's worth checking if they really mean absolutely no make-up, or if they just want a natural look (mineral foundation is great for that), but there's no need to worry if it's the former. If you have really bad skin, maybe just use a BB/CC cream or some sort of primer.