Of course, but people dress up in costumes (i.e. as someone or something else) all the time for plays, at Halloween, etc. It can be done offensively but not always. And Drag Queens are usually playing a character aren't they?
It’s interesting about the costumes. When I was a kid, typical dressing up costumes included a “red indian” or an “Arab” . Not done with any deliberate malice, but you wouldn’t get that now because we realise those familiar characters and costumes were actually just products of our culture with very little connection to or indeed interest in the real lives of the people they purported to depict. “Red Indians” and “Arabs” were ideas that real people made art about, not real people who might themselves make valid art.
So similarly with drag queens. The characters aren’t realised women characters, they are taken from a palette of female stereotypes. Slag, bitch, bimbo, tragic beauty, ice queen, amazon and so on. Not necessarily always insulting stereotypes, but stereotypes nevertheless.
As I said before, not necessarily often consciously misogynist, but definitely not unproblematic.