Can Khajiit become werewolves?
Solution 1:
Yes, you can. I've become a werewolf with my first character, who was a Kahjit melee assassin.
Solution 2:
Yes, characters of any playable race can become a werewolf, including Argonians and Khajiits.
I myself have a werewolf Khajiit, and there is not any problem with this.