I plan on asking my girlfriend if she wouldn't mind shaving her mustache.
What is wrong with her having a mustache.
It's not something nice to put your mouth on.
It is wrong to expect someone to shave their face for you. If you don't like it you can break up and find someone else.
I am not going to break up with her. This is serious.
Well maybe she will be open to shaving her mustache to you. However, trying to force her to do so may just make her upset. It may be better to just let her know that you prefer her to not have it.