I guess this is a factual question? (Even if it turns out to differ from jurisdiction to jurisdiction).
Suppose a caterer had a religious objection to interracial marriages. Can that caterer be compelled to cater an interracial marriage?
What if the caterer’s objections didn’t count as religious objections? Could they be compelled in that case?
He cannot be compelled.
He can be sued for racial discrimination.
Conceivably, Federal charges can be brought.
I’ll let the lawyers get into details.
As for law, being “forced” to perform a specified action is known as “specific performance” and is rarely invoked. Monetary damages are the common remedy under tort law.
And: from Business Law 101: Specific performance can be awarded in matters involving sale of real estate or other non-fungible items.
How could there be a religious objection? I’m just curious as to what religion has codified this, but Og knows I have no sense of theology.
Well, I guess I was speaking very loosely. Maybe I can rephrase as “compelled either to cater the wedding or render damages.”
So would the person likely have to pay damages if they were sued for not catering an interracial marriage?
Well, I know there are religions in the states which espouse white superiority, so it’d be no surprise if they forbade interracial marriages.
The question could be considered as discussing a hypothetical case though.
Which ones?
But it really doesn’t matter. You can propose that as a hypothetical. 
The religious objection to interracial marriage was tried back in the 1950s and 60s. Various white supremacists tried to get around Civil Rights laws by claiming it was part of their deeply held beliefs. Courts didn’t agree.
Well, the old segrationalist argument was the existence of different races is evidence that God intended there to be different races, and therefor any inter-racial marriage goes against God’s will.
Check out the Church of Jesus Christ Aryan, the religious arm of the Aryan Nations.
And Christian Identity.
And the Creativity Movement.
And the 2009 Louisiana interracial marriage incident, where a Justice of the Peace refused to perform an inter-racial marriage based on his personal beliefs.
ETA: have plenty of brain bleach on hand if you browse those cites. You’ll want to do a thorough cleansing of toxins afterwards.
^ This. Religious Freedom protections where they exist are based on there not being a compelling government interest to override the religious objection, and there not being a less intrusive way to meet that government interest. Civil rights protections have made it through those tests. RFRA is not about religions trumping all.
It’s sadly more than hypothetical:
Christian Identity
Kinism
Wotanism (Odinism) - not all Norse derived religions are racist but some are
There’s been movements from racist Christian sects towards Norse style in the last couple decades. Sometimes it might be less creepy to be ignorant.
Some would fall under the label of Christian Identity.
Is that what you’re asking for? I’m a little surprised, I admit, if anyone who lives in the US doesn’t think there are religions in the US which espouse white superiority.
What were these white supremacists being asked to do w.r.t. interracial marriage and which they argued was against their religious beliefs?
Race is a federally protected class in the US and restaurants, considered public accomodations, cannot legally discriminate against them: Discrimination in Public Accommodations - FindLaw
Doesn’t matter what states or religions think. Federal law trumps them.
IANAL, but I doubt there’s a special case for caterers as opposed to restaurants.
(Gayness, which I assume is what this thread is derived from, is not a federally protected class)
… They know he was a Jew, right ?
I’m not saying they’re theologically rigourous in the same way as S Thomas Aquinas or S Augustine. 
These are recognized religions in the US? That is, they have tex exempt status?
There is also idea if they hate race,gender,sex,interracial marriages or gays they may put some thing in the cake or food to make you really sick.
So forcing them to make it for you can you really trust them.
What I don’t get is why the business owners feel the need to explain their motives behind not wanting to service someone.
If the business owners don’t want to serve you because of some religious or what ever reason. Why do they tell the customer;
" I will not cater your wedding because you are gay…" or " because your are two different races…" etc…
Why don’t they say " So sorry we are booked that weekend…" and just leave it at that? and to make sure that there is not any perceived animosity give them the contact info for another caterer?
This whole mess could be avoided if the business owners just lied about being booked. Why open the can of worms by saying out right why… do they feel they have some sort of “righteous” duty to rub their religiosity in you face?
It’s illegal to poison food.
If someone is unwilling to serve the public equally they should not be granted permission to do so. If they can’t be trusted they shouldn’t be in business to begin with.
This is what most do, which makes it nearly impossible to prove.