We're playing the Star Wars RPG but this problem isn't system specific.
It's normal for this group to drop character, usually for jokes and chatter, so that isn't something that can be addressed.
It began as a minor joke, referencing a series of cartoons about a shaven Chewbacca (he gets a Mohawk, a Brazilian, etc.). We spent about 20 minutes one session joking about shaven wookiees during a discussion of disguises. Some bleach and hair dye should be enough to disguise a wookiee.
A couple of sessions later, my character was wounded, and as part of a "medical procedure" to get rid of a critical injury, our medic shaved the character's entire back. Then we spent a while joking about shaving wookiees. I wasn't impressed, but I ignored it. The character later admitted that it wasn't a necessary procedure.
The session after that went normally. No wookiee shaving fetishes.
Then, during the most recent session, the player in question spent more than an hour trying to shave my character, making rolls without prompting from the GM to trick me into getting shaved, and insisting that the latest injury required a full body shave. I'm playing a tank, so of course the character gets injured regularly.
How do I stop this obsession / fetish about shaven wookiees?
The player in question regularly drops character and begins trying to shave my character; if this ongoing joke was truly in character, he would have lost his arms by now.
(P.S.: Don't google "shaven wookiee" at work.)