The correct option is E are often lacking in romantic relationships and although positive intent between partners is a given, it is rare for people from disparate backgrounds to share their lives together.
A) are often lacking in romantic relationships and although positive intent between partners is a given, it is, however, rare for people from disparate backgrounds to spend their lives together. --- although and however are redundant.
(B) are often lacking in romantic relationships and although positive intent between partners is a given, it is rare that people from disparate backgrounds to spend their lives together. ---Where is the verb in the relative clause that follows the main clause ‘it is rare’? To spend is not a verb; it is simply a verbal. This sentence is, in part, a fragment.
(C) is often lacking in romantic relationships and although positive intent between partners is a given, it is rare for people from disparate backgrounds to spend their lives together. --- SV mismatch; the right verb should be ‘are’
(D) are often lacking in romantic relationships and although positive intent between partners is a given, it is, however, rare that people backgrounds spend their lives together. – although and however are redundant
(E) are often lacking in romantic relationships and although positive intent between partners is a given, it is rare for people from disparate backgrounds to share their lives together. – E is the best of the lot with no redundancy and fragmentation.