Equal protection under the law is vital in a democracy. Only through protecting the rights of all can justice be done. A society which ignores the rights of some, can at some future date ignore the rights of others. In order to ensure equal rights for all, all peoples rights must be protected at all times.
Religious institutions and individuals are already afforded the right to freedom of religion as outlined in the constitution. Any other legislation that tries to support religion is infringing on the rights of people to have freedom from religion if they choose. It creates unnessary protection for people whose rights are not being infringed.
The name "Religious Accommodation Act" covered up the intended act of this law, which was to deny accommodations to members of the LGBTQ community in Mississippi. This is similar to the laws that Southern states passed to keep blacks from voting after the Civil War, such as poll taxes, literacy tests (which were actually much harder than simple reading) and the like. There are ways to exercise your religion without discriminating against people on the basis of their gender orientation.
Religious freedom should always be a necessity in the United States and blocking this accommodation act just makes it harder to meet everyone's religious preferences. Religious beliefs are an important part of many peoples life so by blocking this it violates the constitution. Everyone should have access to religious accommodations when necessary.