If the Supreme Court upholds same-sex marriage, would churches be forced to comply?

Only if the SCOTUS found that churches were required to recognize and perform same-sex marriages, which is highly unlikely to be the case.

The issue is with state laws, not churches. Courts are finding that many state laws violate the fundamental right to marry, while other states are overturning their marriage laws by legislative or popular action - rightfully so, because there are NO arguments used against same-sex marriage that were not used against interracial marriage (opposition to which also included arguments based on the Bible which are often ignored today) - there is simply no good reason to continue to prohibit same-sex marriage. If you don't like it, too bad - your discomfort does not trump someone else's fundamental human rights.

If a church is conducting business in the public, yes. For example, say the church sets up a bake sale or car wash on the side of the street to fund raise. They cannot refuse to sell someone a brownie because they are a gay married couple.

If a church is publicly advertising their building or property for rent as a venue for events, they cannot refuse someone because they are a gay married couple.

However, a church will NOT be forced to perform the marriage ceremony of a gay couple. Pastors and churches frequently choose who they will marry or not marry. Many will refuse to perform the ceremony if someone has been divorced, or they feel it is not a god blessed union, or the itch just isnt scratchin for them.

No. Churches don't have to perform marriage ceremonies for anyone they don't want to perform marriage ceremonies for.

The Court ruling applies to the legal part of the marriage ceremony, the certificate you get from the county. The marriage can be performed by a judge and doesn't need a blessing from the church to be legal.

With what?

Yes, churches will be forced to recognize gay married couples as being married.

No, just like with interracial copules, no church will be forced to endorse any marriage they don't approve of. Which means they don't have to perform ceremonies. You can't make someone pretend an imaginary skyman is approving of a marriage. Marriage is a governmental matter, not a religious one, despite people giving cash to priests, parsons, and reverends for such things..

Yes, funny colleges of biblical knowledges, as well as hospitals, if taking government aid or getting government tax breaks will be required to recognize gay marriages. Just like they were forced to recognize a white woman could be married to a black man.

Clergy would be required to perform such rites or loose their legal authority to perform such services. Couples would then be forced to also undergo the marriage ceremony in an otherwise legal or civil venue.

Marriage is a civil act and not a religious one, so it would make no difference.

No However county clerks at local courthouses would.

^^^^ but won't that be breaking the law?

Basically, would this new civil right trump 1st Amendment religious rights?

No because they also have a choice.