As in "jackleg preacher", "jackleg carpenter" or "jackleg mechanic". Although an amateur mechanic is usually a "shade tree mechanic" = no shop, works under a shade tree.
It just means that they are not “active” in their religion, specifically, LDS. Growing up, we learned early that there were Mormons and jack-Mormons, though both are Mormons. The difference being that the jack-Mormons, while not obeying the Commandments and the Word of Wisdom, were still Mormons.
That’s not to say they were always that way. Some lapsed as teens or adults, and some didn’t have the exposure to the teachings as tots.
TC was spot-on when she said it coincided with lapsed Catholics, etc.