Of course you can legitimately love someone with a mental health issues, why on earth would you think you couldn't?
As for would I stay with someone with MH issue? If it wasn't seriously affecting the relationships or my mental health of course.
If I didn't love them, would I stay with them out of obligation though? No chance in hell....not because of their MH. But because I feel 0 obligation or responsibility to stay with people for their mental health. As harsh as it may sound their MH is neither my problem nor my responsibility and I won't give up my life, needs or wants for them.