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The judge is citing the US Constitution's first amendment, which is kinda stupid as that applies only to Congress and the New Mexico Constitution has articles much more applicable and clear:

Art II, Sec. 17. [Freedom of speech and press; libel.] Every person may freely speak, write and publish his sentiments on all subjects, being responsible for the abuse of that right; and no law shall be passed to restrain or abridge the liberty of speech or of the press. In all criminal prosecutions for libels, the truth may be given in evidence to the jury; and if it shall appear to the jury that the matter charged as libelous is true and was pub-
Art II, Sec. 11. [Freedom of religion.] Every man shall be free to worship God according to the dictates of his own conscience, and no person shall ever be molested or denied any civil or political right or privilege on account of his religious opinion or mode of religious worship. No person shall be required to attend any place of worship or support any religious sect or denomination; nor shall any preference be given by law to any religious denomination or mode of worship.
Art II, Sec. 4. [Inherent rights.] All persons are born equally free, and have certain natural, inherent and inalienable rights, among which are the rights of enjoying and defending life and liberty, of acquiring, possessing and protecting property, and of seeking and obtaining safety and happiness.

Art 2, Sec 4 says there are certain inalienable rights among which are those listed — this does not preclude the existence of others, in fact the 'among which' indicates that there are others, such as having one's own opinion (as explicitly stated in respect to religion).