For those of you squawking about how "private" businesses should be able to discriminate, you're wrong. Businesses do not follow the same legal pathways as private properties and residences do. As long as the business projects itself to the general public, whether through its location on Main Street or through its public marketing, it cannot discriminate against any particular group of clientele. That goes for the Westboro Baptist Church and any other group that one might find unsavory.
This non-discrimination law is based in Title II of the Civil Rights Act of 1964. Which is where the sticky subject of sexual orientation comes into play, as the law only refers to race, color, religion, and national origin. However, if you think that the CRA doesn't set precedence for sexual orientation I recommend taking it up with the Supreme Court. Except that, ya know, Supreme Courts are striking these down left and right, so good luck with that. Regardless, bills like Arizona's SB1062 are OBVIOUSLY laws based on the establishment of religion, even if they don't inherently favor a particular denomination, which goes against the very first sentence of the 1st Amendment.
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
Bottom line, a "private" business owner can only discriminate if his/her business is located outside of the public sphere, i.e. no advertising whatsoever, private location, etc.