WASHINGTON — A New Mexico law forbids businesses open to the public to discriminate against gay people. Elaine Huguenin, a photographer, says she has no problem with that — so long as it does not force her to say something she does not believe.

In asking the Supreme Court to hear her challenge to the law, Ms. Huguenin said that she would “gladly serve gays and lesbians — by, for example, providing them with portrait photography,” but that she did not want to tell the stories of same-sex weddings. To make her celebrate something her religion tells her is wrong, she said, would hijack her right to free speech.

So she turned down a request from a lesbian couple, Vanessa Willock and Misti Collinsworth, to document their commitment ceremony. The women, who hired another photographer, filed a discrimination complaint against Ms. Huguenin’s studio, Elane Photography. So far, the studio has lost in the courts.

There are constitutional values on both sides of the case: the couple’s right to equal treatment and Ms. Huguenin’s right to free speech. I asked Louise Melling, a lawyer at the American Civil Liberties Union, which has a distinguished history of championing free speech, how the group had evaluated the case.