There are some limits - looking at it, I suspect I would be allowed to discriminate if I converted a couple of bedrooms of the house I was living in, but not if it involved a separate house.
There was another exception made for religious organizations, but none specified for religious people operating a business. The law also applied only to businesses of a certain size - in 2003, it only applied to businesses with 15 or more employees, but in 2004 it was made to apply to businesses with over 4 employees.
I also found that NM Republicans attempted to overturn the law by referendum in 2004, but there were problems collecting signatures, and the State DA said the HRA fell into a category of law that could not be overturned by referendum.