Sorry, moral objections trump state-imposed laws. Would you have followed a law under Hitler that forced you to seize Jewish property, report on your neighbors, etc?
Really, now?
I have long had a moral objection to paying taxes to this spendthrift government, let's see how far I get with that...
I agree with your assertion, that push come to shove, most people will put a strongly-held moral belief above the law - even to the point of being in violation of the law. It's wishful fantasy on the part of many, if not most lawmakers, that the law is effective at changing hearts and minds.
The poll question isn't useful to discriminate where the responders would draw the line. Ask them if it's okay to steal a loaf of bread to feed a starving child, and the poll will yield the opposite result (even though stealing bread is against the law, and at bottom is, I think, immoral as well).
Should Catholic Charities be compelled to charity? Obviously, that's an oxymoron. Charity that happens only on account of compulsion, or threat of compulsion, isn't charity at all.