Every nation has divisions, I agree. I imagine the majority Sunni population of Syria would rather not have a Shiite minority running their life, but I think the issue of "support" at this point is moot: too many outside influences keeping the pot stirred to get adequate readings.
Personally, I think that "terrorist" is a nebulous smear-tag that will not move any discussion forward. Is it terrorism when the regime opens fire on dissidents, or when the dissidents kill security/soldiers and burn, loot buildings? I'd rather not qualify violence as more good or more evil. Violence sucks, and people suck when they resort to it.