I honestly don’t know enough about them to compare their beliefs to sharia but I think that is a stretch.
The Bible does teach the man is the head of the household and that women should dress modestly and that children should honor their parents. I have no problem with those teachings.
I can see your point, but if you look at what Gothard actually teaches those ideal are distorted and become something else entirely.
Questions of dress and modesty change from society to society and there is no universal indicator of modesty. Unless a mullet and a mumu are in the bible somewhere. :)