The Territorial Authority can't do anything
The Dogs travel in groups of three and have community support. While what they do may not be legal, the territorial authority is, outside of industrial incursions from the East, basically powerless. The Territorial Authority, if there even is any, is probably no more than a Federal Marshall with a junior partner. Dogs is based off of old-west Utah, so this list of 1800s forts in Utah might help explain things to you. Of the 58 fortified settlements erected in Utah during the 1800s, 29 of them were erected by the Mormons. Another one was erected by a fur trading company but bought out by the Mormon church for close to $2,000. Another one was a splinter group that managed to set up a massive fortification in the mountains. The Mormon church raised a private army (the Mormon Militia), stormed the fort, and executed the originator of the attempted religious change along with many of his followers.
In fact, the military might and financial resources of the mormon church in Utah were so great that the federal gov't eventually realized that were the Mormons to rebel there wouldn't be much they could do about it, so in 1858 they (in violation of the 3rd amendment to the US constitution) occupied an existing Mormon fort and much of the surrounding town, eventually leading to the modern city of Fairfield. This was the largest military encampment of federal troops in the entire United States at the time.
In response, the Mormons booby-trapped the canyons the federal troops would use if they were to try to invade the nearby new Mormon settlements, evacuated all the old settlements, burned the army's supply trains, and hid in the mountains. Brigham Young negotiated a peace with the commander of the US forces, whereby the Feds kept to their fort in Fairfield and Salt Lake City remained the capital and the US appointed replacement governer was installed but Young remained pretty much actually in charge.
Much conflict over polygamy ensued.
The point here is that, by analogy, the Faith has far more power than the Territorial authority. If the East decides it's gonna do something about the Faith and invades, yeah, that'd be a force the Faith couldn't handle head-on, and that's what eventually happened in real life, eventually. Short of that, though, the Faith has the military might to enforce its laws as it sees fit. An individual agent can certainly get in the way of the Dogs' work, seeking to enact their Federal Mandate with etic integrity, but that looks a lot more like Hang 'Em High than any sort of one-sided lawman beatdown. The Dogs need to balance the law and the faith because their faith includes tenets regarding obedience to civil law, where moral, and sometimes for other reasons, but not because the TA actually has the power to militarily shut the Faith down.