They insisted that he ____ banned.
...he be banned is the same as he should be banned...it is forceful and compelling giving no room for choice making
"Be". It's the subjunctive!
It's the "they" in the sentence..
You can't have "they was".. Simple.. It's "they be"
It depends on the context. If they are arguing after the even happened whether or not he was banned, you could use "was" (although this is very unlikely).
I am really good at spellings and grammar. I really enjoy it. I do it a lot at home and at school to become really good.