The first song I can recall singing in a female voice was House Of The Rising Sun. It never bothered me till The Animals recorded it and changed the sex of the narrator to male. Not only did the song lose a lot of its meaning, but people who knew the song from The Animals would ask me,"Why did you change it to a woman's song?"
While I am not uncomfortable singing in character, I don't sing songs in dialect, because I don't feel comfortable doing them.
I don't feel bad about singing murder ballads in the voice of the murderer. I'm playing a part.