You're right, it's possible that Mal is a C-subtype. I'm not settled on the subtypes just yet.
[Edit: I checked my master list, and I see that I previously had Mal down as a C-LSE. I'm not sure what I was thinking when I said he was D-LSE -- a momentary lapse, I suppose. ]
People don't normally hate members of the opposite Quadra, particularly if they share a club. Often Contrary and Quasi-Identical types can get along fairly well, especially if they focus on work.
A significant part of the crew's discomfort with Jayne is that he's too aggressive. In my opinion there is also a significant Si/Se conflict, as well as the Fi/Fe one.
What you're seeing there is classic Caregiver behaviour. LSEs can't open up emotionally very well, but they can make up for it by taking care of people's physical needs. Mal never talks about his feelings, but in LSE fashion he shows that he cares by doing practical things to take care of his loved ones. The "You tell me right now little Kaylee, you really think you can do this?" line shows this typical concern for others' physical welfare, coupled with a strong ability to assess others' capabilities in a practical Te sense.
Zoe displays emotion less than Mal does (except when she's alone with Wash). She seems pretty obviously Fe-PoLR to me, or at least 1-d Fe.
Also, I don't see how anyone could type Wash as an Introvert. Other than Kaylee he's the most emotionally extraverted character on the show!
I'm not as sure of Inara's type as I am of the others. I considered IEI for a while, but the intertype relations didn't make sense. I could see someone making the case that she's EII, but for now I think ESI makes more sense.
You'll note, she's not so much a mystical mentor, as she is a relational mentor. She doesn't talk about destiny and the future and the spiritual significance of things, she talks about people and relationships.
Now that I think of it, she could be an Ni-Harmonizing subtype. That would explain the calm, serene energy she has. It would also jive well with Mal being a Creative subtype, as I speculated above. Hmm.