The answer is, look to the Roman Catholics, who manage to teach a lot of things that are different from the culture to which their children are exposed.
On the subject of sex and sexuality, the Roman Catholic church is way out of step with the mainstream of America. The teachings of the church are not only against homosexuality (which isn't working so well, as it is widely accepted a large fraction of the RC priests at least in this country are gay), but against contraception, and against divorce.
Now, let's start with the strictures against contraception: the Church does not actively work in the political sphere to eliminate access to The Pill, condoms, diaphragms or other forms of pregnancy prevention. Although they disapprove, and are very clear on the subject within the church, those who are not RC are free to use whatever means they can to prevent unwanted pregnancy.
Of course, all you need to do is look around inside a Roman Catholic Church to see how well the People of the Church are adhering to that stricture. The days of the big Catholic families with 6 or 8 children are long behind us; I don't think anyone pretends that the majority of the faithful are using the rhythm method.
But here's the thing. Despite the failure of the contraception rule, they (the Institutional Church) are not trying to outlaw contraception.
What about divorce? This one is particularly helpful to consider. The Roman Catholic church is absolutely clear: you cannot divorce and remarry (unless you can afford an annulment, but we won't go there). For the vast majority of Catholics, that means that if they divorce in the civil sphere, they cannot remarry in the church. And that rule IS adhered to, very strongly.
Yet divorce in the civil sphere is legal, as is remarriage. As Andrew Sullivan writes in his excellent essay, Modernity, Faith and Marriage (a MUST READ):
Catholics, for example, accept the word marriage to describe civil marriages that are second marriages, even though their own faith teaches them that those marriages don't actually exist as such. But most Catholics are able to set theological beliefs to one side and accept a theological untruth as a civil fact. ..... Catholics can tolerate fellow citizens who are not Catholic calling their non-marriages marriages - because Catholics have already accepted a civil-religious distinction. They can wear both hats in the public square.
Thus, despite firmly teaching that divorce and remarriage are not allowed, the Roman Catholic church is able to co-exist with a society in which divorce and remarriage are available. They are not advocating for constitutional amendments to outlaw divorce or remarriage. They teach their own values, even if they conflict with the greater society. Because our nation is not a theocracy, and no single religious group gets to make the rules for all.
We really must stress that we are discussing a separation of civil from religious marriage. Religious groups do not get to inflict their definition of marriage onto society at large. The Catholics already accept that for divorce. This is no different.