And then Willfor was the ninja.
But yes, to give a concrete example: I can be an atheist (I'm not) and still find murder against my personal morality, and thus refuse to commit murder. I'd even posit that one can be a pro-life atheist, depending on your personal definition of when life begins.
As stated though, the problem with granting blanket acceptance to things like that is that it could be abused. "Wearing pants is against my morality." "Allowing gays to live is against my morality." "Working is against my morality."
The thing with a religion (for the most part) is that the claims are verifiable and reproducible. If you're Jewish and you claim that eating pork is against your religion, there's plenty of written evidence to support that, as well as a whole lot of other Jews who will back you up on that claim. (There are also plenty of Reformed Jews who will nod while wolfing down that last pork chop, but that's a different story.)
This gets into grey territory when people start using the "religious reasons" loophole and citing obscure and/or personal religions. Like the girl in my area who was expelled for violating school dress code with a nose piercing, who sued and claimed that it was for religious reasons and that her religion was the Church of Body Modification. She won. In her case, there apparently is a recognized organization of that name with about 3500 members.
In theory, I could found the Church of the Red King, come up with whatever theology I want to support whatever it is I want the right to do, then claim religious exemptions to do it. Which is a pretty blatant and cynical manipulation of what those laws were intended to do.