I've brought this up in a couple of other discussions on the HHS mandate.
Does the Federal Government have the right to force Muslim grocers to carry pork in their stores?
Your poll question is not the same thing as the question you ask in your opening post. So let's address them one at a time:
Poll: Can the Federal Government force a business to violate the owners religion?
A bit of a loaded way to word the question but, yes, the federal government can force a business to behave in certain ways contrary to how they might prefer to behave due to their religious beliefs...particularly if there is a compelling public interest at stake in doing so. Sometimes the government will allow a religious exemption, but in many cases they are under no obligation to do so. For example, Quakers are generally exempted from the draft due to their pacifism. Muslim women may or may not be required to remove facial covering for a passport photo, depending on how extensive the covering is. The Amish are not exempted from paying social security taxes (which violates their religious belief against insurance), but the federal government often looks the other way nevertheless. Mormon sects that still believe in polygamy are held to the same laws banning it as everyone else, and the government will NOT usually turn a blind eye to that.
So it depends on the religious belief in question, and how much the public interest is actually advanced by banning it. As for sole proprietorships and other small businesses, it's still essentially a question of individual liberty so I think the same principles would apply for small businesses that apply for individuals.
If we just flat-out declared that the government had no right to cause anyone to act contrary to their religious beliefs under any circumstances, then you'd have all sorts of people flouting all sorts of laws on the supposed basis of their religion. And then the government would be in the far uglier position of determining what counts as a religion and what doesn't. To me that seems far more invasive than just passing laws to benefit the public at large, and (depending on what they are) possibly allowing a religious exemption or possibly not.
Does the Federal Government have the right to force Muslim grocers to carry pork in their stores?
Probably not. There are a couple different issues in play here:
The first is the question of whether or not the federal government has the right to force ANY grocer to carry pork in their stores, irrespective of religious belief. To that question, I think the answer is "probably yes." I'd liken it to the federal government forcing auto companies to sell more fuel-efficient vehicles than they might otherwise be inclined to sell. Whether or not that's a good POLICY is another question, but in terms of law I don't really see any distinction between forcing a grocer to sell pork and forcing GM to sell more efficient cars.
On the question of how it affects the grocer's religious beliefs, as I mentioned above there are plenty of cases where the public interest contradicts with individual religious beliefs...and in most cases the public interest wins. So there's not any inherent red-line that would prevent the government from forcing a Muslim grocer to sell pork. The more important question is whether it actually advances the public interest. It's hard to make the case that forcing a Muslim grocer to provide pork is a compelling public interest that trumps the owner's religious liberty, as pork is not exactly a health food. And even if it was, it would probably be hard to make that case if there were plenty of other groceries that were willing to sell the product and plenty of substitute products.
So the fact that there's no real public interest at stake here would make me say that the government probably CAN'T force the grocer to carry pork, as it stands now. But if it were discovered tomorrow that eating pork was a miracle food which prevented all forms of cancer and heart disease, and studies showed that many Americans live in areas where the only nearby grocer refuses to carry it due to his religious beliefs? My verdict would be yes, the government IS able to force them to carry pork under such circumstances.