A somewhat similar dispute has been in the news periodically concerning anti-abortion pharmacists who object to having to sell the morning after pill. I think a couple of cases went to court and they lost. Basically, the courts are not going to give someone the right not to perform an essential job requirement just because it is claimed to infringe on their religion. If the employer can accommodate them without a lot of burden, different story. Clearly the employer has an unreasonable burden if employees are free to decide they won't do routine transactions.
These are relatively easy cases. What about a ob/gyn doctor who refuses to perform abortions? What about a lawyer who is required to handle a case to bar a Ten Commandments display? These seem to me to go beyond routine transactions and require the employer to participate in activity he considers sinful. It's easy to say, get someone else to do it, but what if it is a small country hospital or a two man law firm? Can your business be ruined by a mere employee's religious sensitivity?
The problem with devout muslims is the vast array of activities they object to. What if the clerk refused to serve women who weren't veiled? Given the opportunity, they try to turn religious accommodation from a shield into a sword to force everyone else to observe their religious edicts. Then they begin to demand the right to run their own communities pursuant to islamic law. They have already done this in the UK. Of course, we already allow illegal mexican immigrants to do this, so why should they be any different.