In looking for a new club, my two criteria were "no touching" and "no nude lap dances." I don't mind doing nude stage dances because if a guy tries to pull any shenanigans, a bouncer will move in and kick him out. Lap dances, however, are nowhere near as heavily monitored. You basically have to fend for yourself in a lap dance unless the club is prestigious enough to have a member of security watching at all times.
I honestly don't mind doing lap dances - I even enjoy them with a fun, respectful guy, and it's where we make most of our money - but I personally wouldn't go full nude in a lap dance for two reasons:
1) The obvious; a few rare guys don't see strippers as human, but rather as objects to grope and do whatever they want to them. The fingers and tongue will come out and they completely disregard the no touching policy (if any), and they will counter any protests of yours with, "I was about to leave anyway," "You're no fun," or "Stop being a b*tch." These exist in any club, regardless of the level of nudity, but leaving a thong on during lap dances reduces the risk of successful genital violation.
And 2) Taking my thong off during lap dances limits what I am able to do. If I take my thong off, I can't grind on the guy's lap. It's not very sanitary to rub my bare genitals on a guy's pants; I don't want to risk getting a bladder infection or something similar from getting dirt and lint in there. I also would not be comfortable humping a guy's face without a thong on - it's a fun trick for getting the guys aroused quickly, which means more tips. I like being able to give a raunchy lap dance, but I believe that leaving my thong on is critical to keeping it safe.
So, nude lap dances are a big dealbreaker according to my personal comfort level. But that's just me, and it's a decision you should make for yourself. If you're not comfortable, it will show in your dancing and in the way you carry yourself. As far as I'm aware, a club can't actually force you to take your thong off, much as they make you think they can. If I were you, I'd see if they have a problem with you doing lap dances with your thong on (many of the girls might do that already), if that's what makes you most comfortable. I know a lot of full-nude clubs don't have a problem with girls leaving their thongs on for dances. It may affect the money and it may not; depending on the club it may not matter, you may still make plenty of money.