Is forcing people to work for others when they don't want to a form of slavery?

This last week the New Mexico Supreme Court ruled that Christian photographers can't decline certain customers based on their religious beliefs.  Personally, I don't know how this gets around the "free exercise" clause in the First 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.

The New Mexican Supreme Court claims that forcing someone to violate their religious beliefs is just "the price of citizenship."

Why is government prevented from newspapers forcing to carry opposing views but perfectly OK for the government to force people to provide their time for causes that they think are wrong?  Jonathan Turley has a differing view available here. 

Add this to the growing list of controls that government has over people's lives.  For example, Obama is threatening jail to someone who wants to shutdown his business rather than turnover information on his clients to the government.