The guts of the issue, right here in Elane Photography V Willcock:
{55}
Elane Photography also suggests that enforcing the NMHRA (New Mexico's anti-discrimination law) against it would mean that an African-American photographer could not legally refuse to photograph a Ku Klux Klan rally. This hypothetical suffers from the reality that political views and political group membership, including membership in the Klan, are not protected categories under the NMHRA. See § 28-1-7(F) (prohibiting public accommodation discrimination based on “race, religion, color, national origin, ancestry, sex, sexual orientation, gender identity, spousal affiliation or physical or mental handicap”. Therefore, an African-American could decline to photograph a Ku Klux Klan rally. However, the point is well-taken when the roles in the hypothetical are reversed—a Ku Klux Klan member who operates a photography business as a public accommodation would be compelled to photograph an African-American under the NMHRA. This result is required by the NMHRA, which seeks to promote equal rights and access to public accommodations by prohibiting discrimination based on certain specified protected classifications.
{56} However, adoption of Elane Photography’s argument would
allow a photographer who was a Klan member to refuse to photograph an African-American customer’s wedding, graduation, newborn child, or other event if the photographer felt that the photographs would cast African-Americans in a positive light or be interpreted as the photographer’s endorsement of African-Americans. A holding that the First Amendment mandates an exception to public accommodations laws for commercial photographers would license commercial photographers to freely discriminate against any protected class on the basis that the photographer was only exercising his or her right not to express a viewpoint with which he or she disagrees. Such a holding would undermine all of the protections provided by anti-discrimination laws.
It is painfully obvious that people arguing against the gay couple do not know what a public accommodation is and why public accommodations are subject to anti-discriminatory laws, such as the Civil Rights act of 1964.