Marriage without love is meaningless.They are free to marry any member of the opposite sex they choose, just like heterosexual couples.
Then the system need to be changed, so that love is the most important aspect of it. And when love is, the kind of system you talk about only appear insane.There are no privileges lost, they just don't get the same privileges because they wish to behave in a way that is contrary to why the extra privileges of marriage were given in the first place.