Mrs. Potts being the stereotypical ESE kind of overbearing mother. (she could also be SEI I suppose but I lean towards ESE) All of the other/main protagonists are beta - Belle, Beast, Lumiere, Cogsworth, and Chip.
Lumiere - EIE
Cogsworth - LSI
These two definitely fit the Beta rational duality that some here have experienced or witnessed. Lumiere is almost the star of the show it seems lol. Be Our Guest seems like a showy beta song too. Also note the beta views of alpha when maurice came in the castle acting all careless and everything - I don't remember what he did to lumiere but I remember him twisting the crown behind cogsworth lol
Chip - IEI. I think he is Belle's identical, as he looks up to her, and was so upset about her leaving that he secretly came with when she left to see her father. And he possibly supervises his mom.. Not that it's very visible because he's so young but it was just a vague impression that he didn't take his mom very seriously when she reprimanded him.. Mostly I just think he's Belle's identical because of what I said before, and because he's obviously Fe creative.. SEI isn't totally ruled out but I doubt it.
Gaston - I'm surprised (well, kind of) at how few people here realize that this is how unhealthy LSEs act. The entire town is like deltaland and he's their hero and Belle is the only one who sees through him. Gaston is small minded and chauvinistic, which is how many LSEs can be - especially in the eyes of their conflictor.
Le Fou - IEE. Lets gaston walk all over him.. I would say EII because of that but he seems EP, especially Ne base.
Beast - beta ST
I'm going to add some quotes in and finish this later, I'm tired lol