This has constitutional challenge written all over it.
The problem is that since SCOTUS has criminalized dissent of the recognition of homosexual marriage then is dare not actually condemn discrimination against those who refuse to implicitly sanction/foster homosexual relations.
Even with Masterpiece bakery, in which the baker refused to be complicit in recognizing homosexual marriage (by creating a special work for that express purpose), consistent with the Word of God as well as the CO state constitution at the time, SCOTUS would not send a clear message that the persecution of him was wrong, that a business cannot be forced to go against its conscience in a precise situation as this, but made it seem like the real problem was the antagonistic manner by which the state persecuted him.
Now we have state governments that penalize those who oppose homosexual relations by way of support of traditional family values, even though they do not discriminate against homosexuals (if Chick-fil-A created custom works, or was a function hall, they would have to discriminate to be consistent with Biblical morals),
The doubt if SCOTUS would want to take a case of discrimination against Chick-fil-Am, since having made the bed they do not want to sleep in it.