Would you date a bi-sexual person who has had serious relationships with the same sex?

So if you're a girl, date a guy who once had a long term relationship with a man.
If you're a man, a girl who once had a long term relationship with a woman.

I think that despite people being very 'pro gay' these days, it would make it a little more troublesome.

Like will they still need a little 'action on the side' because of their bisexuality?

Would you allow this 'open relationship?' If not, could you trust them?

Also if they were to leave you and return to someone of the same sex, that might be strange.

I think a lot of guys take it hard when their woman leaves them for another woman.