The shrink may not understand it, but I do. There I recognize my childhood.
Asperger and ENTP and popular.
I think you are quite right about the Ne.
It remains to be seen if she will remain Ne dominant after puberty.
I find it very odd that an ISTP should be interested in religion at all. The ISTP is not counter culture, therefore I take it his religion is the usual brand of Christianity.
It is even more odd that he insists that everybody follows his lead. This does not sound like an ISTP description at all. They are usually very set back.
On the other hand they do conform to the peer group. And more than that, the peer group is everything for them. I am still puzzled that the peer group should be a religious group. It has to be of long standing.
Actually, his religion was Jehovah's Witnesses, far from the norm. He got into it mainly as a crutch after my mom left him years ago. Those guys turned up on his doorstep when he was the most vulnerable (as they tend to do) and hooked him in with all the things he wanted to hear: no it's not your fault your wife left you, it's because Satan is ruling this world. Come with us, follow our rules, and everything will be better. He was isolated and alone and down and they gave him a 'family' when my mom took his away.
He didn't insist that everyone follow it, just us kids. His thinking was that as our father, it's his job to do what's best for us, and since he totally believed that following that religion would lead to us all being together on a paradise earth one day, it was really important to him that we followed it. He couldn't understand our points of view, and his peers in the congregation of course only reinforced the view that it was important to 'bring us round' and that we'd thank him for it in the end. Of course they had no idea how extreme the means were that he was using on us, as I'm sure even they would've condemned that.
I'm very sure he was ISTP though. I - he spent looooong periods completely alone and took a job as a truck driver, saying the thing he liked most about it was being able to be alone on the road for long periods. He was also the stereotypical handyman, obsessed with engines and vehicles of various kinds, and a highly skilled crafstman. He was, in most matters other than his religion (which was only in the last 20 years of his life), pretty laid back and laissez-faire.
But I've known some other ISTP's to be surprisingly rigid about some of their opinions, and quite judgemental of people who don't share them. My step-dad for example is also ISTP and he's as laid back as they come, but if you start him off on the Arabs or his football team, he can easily rival any SJ for rigidity.