Who has the right to marry is limited by the cultural background which is inherently discriminating.
I wouldn't take that for granted. "Fundamental rights," such as marriage, may be "limited by the cultural background," because they are those rights which are "'implicit in the concept of ordered liberty', or 'deeply rooted in this Nation's history and tradition.'" But it's at least arguably true that, despite that foundation in tradition, the rights should be interpreted more broadly--such as encompassing same-sex marriage.
A muslim woman doesn't have the right to marry multiple men or women. She would be put into jail. It is a privilege.
Btw, aren't homosexuals allowed to marry? Its "just" not endorsed by the state?
In American law, rights--even fundamental rights--are not absolute. The government can still infringe on them if it has really good reasons for doing so and doesn't do so more than necessary (to put the
strict scrutiny test in layman's terms). So there are a few ways to approach how polygamy fits in with the notion of marriage-as-fundamental-right: in the first way, we might deny that
polygamous marriage is a fundamental right, while still saying that
non-polygamous marriage
is a fundamental right. Or, we might say that, yes, polygamous marriage is part of the fundamental right to marry, but the government has good reasons to prohibit it and infringes those rights no more than necessary. Or, we might say that polygamous marriage is part of the fundamental right to marry, and the government
doesn't have good reasons for prohibiting it, or infringes those rights excessively. In that last case, of course, a prohibition on polygamy should be struck down.
But none of this means that marriage is a privilege which has the government as its origin. The government couldn't just one day decide that nobody can marry. (Of course, this does
not mean that the government has to endorse any marriage, or extend any benefits to married couples on account of their marital status.)