What they are arguing for, after all, is the view that the First Amendment—by itself, regardless of what statutes Congress (or a state legislature) may enact to protect the practice of religion—requires judges to carve out exemptions to laws for religious believers. The difficulty for this position is that the courts did not take or act on this view for almost the entirety of American history.
In Reynolds v. United States (1879), the Supreme Court upheld a congressional enactment against polygamy over the objection of religious dissidents. When Congress passed the Volstead Act to implement Prohibition, the statute itself included a religious exemption: No court created one. Even in 1943, when the Supreme Court ruled for Jehovah’s Witnesses who objected to having to salute the U.S. flag, it did not give them an exemption from compulsory-salute laws: It threw out the laws altogether as infringements on free speech.
The idea that the First Amendment required (or even authorized) judicial exemptions from laws for religious believers entered the law only in 1963 (and exited it in 1990, when Scalia wrote his opinion). The career of this idea is, that is, nearly coterminous with the high point of Warren Court judicial activism that conservatives usually decry.