It's really better that they not be able to discriminate against customers, especially under the umbrella of religious principles. One of the primary themes guiding those who want that right relates to not "participating in the sin" of gay marriage. Gays have received the sole brunt of the focus, but if the point is to deny customers on the basis of religious principle you have to fairly take into account all the sins and religious principles one might "participate in" by entering into commerce. Along with the dubious "sin" of homosexuality (which has yet to be explained to my satisfaction) there are very real, unambiguous sins that the bible is pretty clear about yet which Christians have been mysteriously uinterested in discussing, such as gluttony, adultery, working on the sabbath, dishonoring your mother and father, greed, sloth, wrath, envy, pride. But wait! There's more! Be sure to memorize each of these six hundred and sixty seven sins. I'll wait.
SIN LIST
Got all that?
Giving people the right to discriminate based on their religious principles is tantamount to giving Christians, the largest demographic in this country, effective tyranny over the rest of the populace. People especially in extremely religious parts of the country would have to cower in fear of businesses turning them away because of some perceived sin. But when you consider how often you hear from those who want the right to discriminate that the United States is a "Christian Country," I'm pretty sure that no vision of the future could fill them with more delight.
It isn't just that gays have received the sole focus in this issue, which has only served to misrepresent the sheer scale of potential for abuse. We've also focused for some reason on pizza and cakes to such a degree that a visitor from a foreign country could be forgiven for thinking pizza and cake were the only businesses operating in the United States. There are also supermarkets, banks, universities, private schools, investment firms, shipping stores, storage units, taxis, pharmacies, major outlet centers, clothing stores, well, you can use your imagination. A disapproved of minority or those not practicing the right faith could find oneself completely marginalized and disenfranchised in the wrong part of the country overnight.
That is a real, tangible damage that can be observed and weighed, whereas the damage of doing business with one you consider "sinful" is intangible and more than likely entirely in the head of the business owner.