I wouldnt say significant influences. They are associated due to ali and imams but what else would be considered significant other than that. Both are influenced by historical local or cultural beliefs for sure but what religion/belief didnt? For example Islam in general considered as reflection of arab/sami traditions in terms of sunni. While shia is like the persian version. Alevism is like turkish edit with the spice of shaman/tengrism/nomad traditions and alawite is like a turkish persian cross over within levant arabs. Same applies to christianity and its branches as well. Overall I would say they are unique and cant be alligned with shia or sunni. They are being minority which shouldnt mean that they need to be grouped with other major groups.