Hello! I just so happen to be genderfluid, though you may want others to give their input since mine is just one pov. ^^
This honestly sounds fine to me as someone that def goes from one gender feel to another, and there are some games that already support changing your customizable MC in the middle of the narrative. The premise honestly sounds fine to me, though the exact nature of the tasks MC needs to do may make it problematic or not depending on what they are.
I appreciate you asking this question to make sure, though! :D