Should a believer in Shinto be allowed to have a Gay Marriage?

If someone believed in Shinto (it's not a cult, it's the one most common religions in all of Japan. It's older than Christianity.) should they be allowed to have a gay marriage? Their Holy text say nothing about homosexuality being wrong. Would it break the first amendment (freedom of religion) to force our christian beliefs on this hypothetical person?
I admit I'm not an expert on Shinto, but say I'm right and it does approve of gay marriage.

what does Shinto say about it,
or can i be its god

If it's OK with them why should I care?

Many people of the christian faith believe it is OK to have gay marriage, even though the bible says not to. If there are no specific rules against it, i see no reason why not. Even if there were, i have a hard time believing that any god would want people to be miserable without someone to share their life with.

Anybody should be allowed to have a gay marriage.

Most of Shinto does not have holy word or bible, so there is no detailed restriction of must/must not or should/should not. So homosexuality is not banned in Shinto. It also means Shinto does not willingly allow homosexuality. Shinto is vague religion.

So in Japan, homosexuality and gay marriage is not religious matter in general. It is left to laws and common sense. I'm Japanese so I don't know much about US constitution but IMO , it seems little bit difficult for Shinto person to influence laws and gay marriage. I think it's not so different from other religions when it comes to this matter.