I'm muslim, and practicing, and come from a very religious family, so for me, I would see nothing wrong with it because marriages are allowed along as they are with "people of the book" i.e. Christians or Jews. However, I think the man has to be Muslim so he'd have to convert if the marriage was to be seen as fully halal per se. However, I don't think it would be bad, or she'd get backlash because if she did an istikhara, she'd know for herself whether a marriage would be good.
But Allah has a path for all of us, so at the end of the day, if things dont work out, then Allah has a greater thing planned.