What other religions (cults) are there that absolutely forbid outside research on threat of punishment / shunning?
Some people have mentioned Scientology and the Mormon church. I could mention a number of these groups, but I think it's the wrong approach. Based on what I know, the label cult doesn't describe exactly what you may want to convey, which is a practice that ranges from simply hiding facts, to discouraging members from researching, to have it as a rule not to do research, to shame, mock, shun or ridicule people who do research, to punish people for doing research, to kill people for doing research. If you see, there are degrees of severity in which such groups apply or enforce their control over others.
As such, it's not easy to just identify one group, hence, there are different opinions about the Mormon church falling into that category. Professionals in the area of those types of groups say that there's not such "list" of groups that take such actions due to labeling being misleading (hence, they may get in legal trouble for doing so), and also because the degree to which such actions are taken and applied to followers, along with the way those actions are applied considerably vary.
However, that said, here are some groups, some of them no longer existing, where people I know have mention had such strict rules against people researching what they claim/teach, or researching about who they really are:
- The Westboro Baptist Church - I met one of the children of the founder of that church (those are the loonies that boycott military funerals and run the "gay hates fags" website), who left. He was completely isolated from the world and severely depressed. When i met him he was in the process of learning basic social skills and working on facing his fears around doing simple ordinary things that he was not allowed to do growing up in the family of the founder of that church.
- Some Karate-based "school" in Pennsylvania (the name of it escapes my mid) - Members who questioned that "school's" methodology, "learning lessons" and coerced inappropriate physical contact between members were beaten by all the members. One of them ended up in a comma.
- The Black Hebrew Israelites - Those are the loonies that stand in cities yelling nonsense about the "White Devil". If you join them and want to leave (or decided to make contact with your own family), or if you ask one too many questions, especially if shaming you doesn't work, you get punished. I met the woman who lost her son to them.
- The International Society for Krishna Consciousness - Those are the ones who dress in orange tunics and go around singing. People who questioned their leadership will go without food and/or water. They have rules around everything and nobody is to question them, or else.
- The WT Bible and Track Society - They have judicial committees, a system of reprovals, and mostly manipulate and keep people at bay by gossip and rumors. They convince people that not doing as they are told will earn them living outside their "spiritual paradise" and will... well, I think you know the rest.
- AAA - This group claimed to be a spin off of AA (Alcoholics Anonymous). They claim to have achieved excellent results with their improved version of the 12-step approach to people who are in recovery from alcohol and/or drug abuse, except for the fact that they (a) separate men and women from their spouses (b) physically punish people who are sinful (girls who are too pretty, boys who are not too masculine, etc.). They manipulate byhaving their members not question a single thing. If they do, they throw on their faces that "AAA saved you from drugs" and the shaming and manipulation goes on and on.
- John Muhammad and Lee Malvo - those are the people later known as "the Beltway Snipers". - Lee, under the influence of John, Lee felt into a disassociate state when he became a co-perpretator in the crimes committed by them both. Lee was convinced that as his "child-soldier" he was going to be "dishonorably executed" if he did not follow the rules imposed by John.
- Some paramilitary Christian Group in Virginia - Those who want to leave or question the leadership of that group get beaten, cut with knives and leaf in the woods to die. I met one survivor from that group who was left to die. Her story is heart breaking, especially since she still has people in that cult.
- Some other Christian cult in New York and Florida - The consequences of researching or questioning anything was having you and your entire family sexually assaulted, all of them, including babies, children, males and females. I met a couple who escaped that group (and yes, they were both sexually assaulted). They were married when I met them, but the guy had a different wife while in the cult. He was in a bitter custody battle of his son. His former wife was still in the cult and allegedly wanted to keep the son there, but the truth was that the real reason was that she was going to suffer consequences in the cult if she lost the custody battle.
- An organization I prefer not to mention - This group in New Jersey and Pennsylvania convinced parents that their children had severe discipline, drug and learning problems. They would be sent their children to them, parents will pay a lot of money to "help their children". The children were kept in captivity. Nancy Regan with her ridiculous, laughable "just say no to drugs" campaign visited that place in the early 80s where they put up a great show for her. A year later 3 children were dead, and all of them were malnourished and living in horrible conditions. The place was finally shut down and the owners were prosecuted. Being there was already reason to get punished, so no need to even do any research.
- Eric Witte - under the influence of her mother, this guy killed his father and helps burying the dismembered body of his grandmother. The consequences of not "doing what mother said" were that everything bad in the family was his fault.
Then there are the ones that made the news:
- Heaven's Gate
- Free Domain Radio (considered the first Internet-based cult)
- Jim Jones and his church
- David Koresh and the Davidian sect
- Jeffrey Lundgren
I hope this shed some light. Cults are not to be taken lightly.