Throughout history, marriage has had many different meanings, but under capitalism, a civil marriage is a voluntary, secular, legal contract between two individual adults, which establishes specific legal rights and obligations between the partners (spouses) recognizing the couple as a single unit before the law.
The right for individuals to civilly marry, regardless of sex, is protected under capitalism. Some private institutions may not recognize the marriage. For example, some religious institutions may not recognize the homosexual marriage within their church. Or, a private wedding photography may refuse to photograph their wedding. However, the partners in a homosexual marriage will receive the same treatment before the law as those in heterosexual marriages.
The right for individuals of different races to civilly marry each other is protected under capitalism. This marriage may not be recognized by some private institutions, but it is recognized by the government and the law. For example, a racist organization can verbally oppose such marriages as “corrupting society,” or the mother and father may only want their daughter to marry someone of the same race.
The right for individuals of different religions to civilly marry each other is protected under capitalism. This marriage may not be recognized by certain private institutions (for example some religious institutions who are free to not provide private benefits to the interfaith couple if they chose to do so, i.e., recognition of the marriage within a church), but it is recognized by the government and the law.