The "show" is actually not bad as a mostly fiction story. I am a member of the church of Jesus Christ of Latter Day Saints (mormon). I do not know the Lafferty family as this happened in 1984 2 years after I was born.
The history (factual) is that the Lafferty family was completely excommunicated from the Latter-Day Saints Church and had begun subscribing to a new fundamentalist belief of an offshoot of extremists, the "School of the Prophets", with Ron claiming he had received a revelation from God telling him to "remove" Brenda and Erica, and spill their blood. Pretty sick people but they were not mormon.
As for the culture and portrayal of the church i grew up in, to me its not acurate at all. I have never felt less superior to a man, men in the church have beards all the time, the women are not hushed and told to be obedient, there is most definitely no Polygamy as it is wrong, there is no animal sacrifices either, all of these things were a part of the split off to what they told themselves were all in God's name.
That being said it was a good show to watch for theatrical elements. Just not factual that they were members of the "mormon" church. If thats what they are going for its inaccurate.