The Satanic Temple is a non-theistic organisation that uses the figure of Satan to test whether religious liberty in the United States is available on equal terms, and its method is to take the state at its word.
If a legislature permits a Christian monument on public land, the Temple applies to place a Baphomet statue beside it. If a school district permits after-school Christian clubs, it applies to run an After School Satan Club. If a state grants religious exemptions from medical regulation, it argues that its own tenets exempt its members too. The point in each case is not the statue. The point is that the authority must either allow it or concede that its accommodation was never neutral.
The Temple is explicitly atheistic. Satan is a literary figure, the rebel against arbitrary authority, taken largely from Milton and the Romantics, and not a being. Its Seven Fundamental Tenets are the nearest thing it has to a doctrine: they commit members to compassion, to the pursuit of justice, to the inviolability of one's own body, to the freedom of others including the freedom to offend, to conforming belief to the best scientific understanding, to rectifying one's mistakes, and to treating every tenet as a guiding principle rather than a rule.
That fifth tenet is the doctrinal statement of the organisation's naturalism. A religion whose nearest thing to a scripture instructs its adherents to follow the evidence wherever it goes is an unusual object, and an entirely intentional one.