Race, color, gender, and disability are off limits (as indicators themselves, not in any correlative or derived senses...). National origin too (but not citizenship). This is the domain of civil rights.
Discrimination based upon ANY action should be fair game. That would include creed...
The problem with your proposal here is that much of the impetus for civil rights law--indeed a basis for the settling and founding of America itself, was freedom of religion. Longtime endemic persecution of Jews (banning ownership by Jews is in many, many deeds, for property titles over 60 years old), or banning Roman Catholic Irish, or Mormons, etc--all of this was a part of pre-civil-rights-law America.
I think it is a very good thing that secular businesses are not allowed to discriminate against religion. Allow "Discrimination based upon ANY action" including "creed", and a lot of evangelical Christians would get fired, as the anti-religious discrimination laws are the only ones that protect them now (if imperfectly) from the homosexual/and liberal atheistic lobby.
We definitely need to keep legal protections prohibiting discrimination based on creed, even though, the increasing number of members of a violent ideology/theocracy/quasi-religion (called ROP here in FReeperland) does make that a challenge. Keeping the current federal civil-rights standards will work--if we can, as conservatives hold back the forces wanting to add (who've already done so on local and state levels) "sexual orientation" to the list. Adding that, functionally nullifies freedom of religion.
If you believe strongly enough in "freedom of association" than logically there should be no discrimination laws at all, be it about non-behavioral or behavioral characteristics.
If their religion prevents them from touching pork, working on Saturday or Sunday, refusing to serve or transport booze, not giving lap dances, dispense condoms, etc etc etc etc etc, then the employer offering a position for which such activities are required should be able to not hire them, or outright terminate them when the refusal to perform the necessary job function becomes evident (ie if initially withheld to obtain the position). Creed should not be used a civil rights shield in such regards. Freedom of religion, not freedom from religion (a distinction carrying weight in both directions - the right of person A to practice their religion does not, or at least should not, impose upon person B the requirement to accommodate it). Sorry that this was not clear above.