Are there any religions or denominations that accept the idea of gay marriage as a civil concept while still refusing to sanctify it within their own church? In other words, they don’t protest the right of a gay couple to obtain a marriage license, but there is no way one of their clergy would ever sign one.
Well, Amish groups who believe in separation from civil society generally don’t vote in elections. So I guess you might say that while they don’t recognize gay marriage in their own denomination, they don’t functionally oppose it for other people.
Generally speaking, though, religious groups don’t bother making official doctrinal pronouncements to put out the message that while they don’t like doing X themselves, they don’t really give a whoop if other people want to do X.
I believe the OP is an accurate summary of the position of the Anglican church of Canada, with the added point that the ACC is studying the blessings of same- sex unions in the Church.
Somehow I’m not surprised the answer would be Canadians.
Some Jewish groups. I mean, right now the Conservative synagogues can perform ceremonies at their own discretion. As far as I know, they aren’t forced to.
Depends on the country.
The Spanish RCC accepts the existence of civil SSM same as they accept that of civil divorce and of civil marriage; that doesn’t mean the RCC itself grants either SSM or divorces. At the same time, the Spanish RCC can recognize marriages which are not recognized by the Spanish government. Switzerland has no civil SSM, but the RCC there accepts civil marriage and civil divorce (in fact, the civil registry in Basel, one of Switzerland’s Catholic cantons, claims to be the oldest one in the world).
Part of the problem in the US and other English-speaking countries is that most people there have no mental differentiation between civil and theological marriage. In countries which have been differentiating both for some 200 years, the mental structures separating them are already in place for “man-and-woman marriage”.
Hindu here. IMHO Hinduism is not really a religion - more like a loosely defined set of guidelines.
In Hinduism, clergy is not needed to get married - (once again different Hindus may hold different views and they are all valid for themselves). As far as I understand, two individuals (a guy and a gal conventionally) can get married and they do not need a witness - fire can be their witness. Clergy or society has no business here. This is not a common practice though in India and priests do preside over marriages - but they are more like facilitators and not the grantor of the marriage license or equivalent.
Actually, this is how most of the Jewish laws work. Even the most observant Jew doesn’t really care about gentiles eating shellfish or wearing mixed-fabric clothes-- Those restrictions are for Jews and Jews alone.
I think you will find that most mainstream churches in Australia agree with the idea that same sex civil unions can take place, they just don’t call it marriage and in fact some disapprove and may lobby for changes.
This page may be of interest: Blessing of same-sex unions in Christian churches - Wikipedia
That may or may not be what you’re after, as those are churches that will bless civil unions, but don’t perform actual same-sex marriages (well, except for the ones that do). I would guess that most of the churches that bless civil unions probably aren’t going to be actively lobbying against SSM, even if they don’t actually perform them.
Well, our churches have had nine years to get used to it! 
However, there is a whole set of laws called the Noahide Laws and one of the prohibitions there is against so-called “sexual immortality.”
In the case of the Orthodox, although there is the rare dissenting rabbi, the umbrella organizations actively fight LGBT rights. The Reform, Reconstructionist, and Humanistic denominations, on the other hand, don’t have a problem with LGBTs.
The Conservative movement fulfills the criteria the OP set out. They have three theological positions which they allow their respective congregations to adopt: 1) Same sex unions are permissible, but anal sex isn’t. 2) Homosexual activity is forbidden and 3) Homosexual activity is forbidden and homosexuals should seek therapy. However, when it comes to the civil concept: “Marriage being both a religious and a civil status, The United Synagogue of Conservative Judaism does not support any action by the federal government or by any state or local government that discriminates and denies equal protection of the civil laws to gay and lesbian Americans who seek to have relationships recognized when they fall within the bounds of the civil law.”
This was my thought too. If that church’s view of morality is that sex outside of marriage is allowed for gays, then where does it stop? Can the minister have a flock of 18-year-old honeys who cater to his needs of the flesh? Or just one? Is cohabitation outside of marriage OK for straight couples? Casual sex? Why should gay people be allowed to indulge in behaviour that was viewed as immoral between straight people?
IIRC this was the issue in the Catholic church (their position, not the activity of some priests); being gay itself was OK because this was a cross some people had to bear, doing something about it was not, since you could not be gay-married and any sex outside of marriage was not OK.
So allowing gays to act out their feelings means you have to define a whole different set of morality, it seems to me. OTOH, most people have ignored thier church’s stance on straight sex for decades (or been hypocrites), why should they care what a chuch says about gay marriage?
The Church of Scotland allows gay (male and female) ministers, including those in civil unions, but opposes gay marriage. Given that something like 60% of Scots feel that gay people should be allowed to marry, I can see the General Assembly (who have the final say on all matters CoS) changing this stance in a few years.