The person who invites the other person on the date should be the one who pays the bill, by default. Regardless of their genitalia or income level.
If a heterosexual man expects a heterosexual woman to go out of her way to wear nice hair and makeup for him on a date, then he's probably not worth her time/energy in the long run.
Of course, I'm gay and only date other guys...and gay/lesbian couples are rendered so invisible and insignificant within society that straight couples tell us we should just "take turns paying" based on our same-sex relationship status per se.