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.)
I like how you rationalized religious privilege while denying the right of Atheists to have any of their moral values acknowledged as worthy of similar protection. Although it is rather strange that you both recognize how morality can divorce itself from religion (Jews eating pork) and yet seem to argue in its favor as something to be protected on basis of shared beliefs. Did I read you wrong? Your argument also seems to ignore that, if one simply needs to point out a common belief system, secular organizations could equally form and say "yeah, this falls under a shared idea of morality."
Maybe the better answer is to throw out the whole thing? Heck, two of the examples you gave for abuse are actually covered by Abrahamic religious tradition already, and we clearly don't protect the second because, thankfully, not even religion's sanctity in our society is enough to allow such monstrosity a serious hold in our culture. Instead it exports itself to African countries... but at least we don't allow it here. The "against my morality to work" thing is however protected, and I believe even was once enforced in some locations, although only on the Sabbath. It isn't much of an abuse though, since not working means not getting paid.
I think what I was trying to get at is that atheists can have perfectly valid moral objections similar to religious objections. The problem lies in how you legally codify that, because morality is a much more individualized concept, and if you extend equal protection to individual morality, it's prone to the sort of abuses I pointed out.
Granted, truly off the wall abuses are unlikely to be protected, in the same way that some religious exemptions/obligations that go strongly against the mainstream are either not protected (stoning non-secular offenders to death, polygamy) or are strictly regulated (use of hallucinogens, animal sacrifice).
I'm not arguing one way or the other in terms of atheists' rights as far as exemptions go, I'm pointing out that it's a thorny issue.