Yes there are many variables involved in relationships. Rising sign IS our Persona, that character we don when around others. your rising sign is also important because it sets out houses, those major parts of our lives. What signs are on the cusps of the houses and , consequently, which planets occupy ( or 'Lord' ) these houses determine . The rising sign is complemented by ones descendant sign, the sign on the cusp of the 7th house of partners and relationships. Like an Aries rising native will naturally be attracted to the Libra rising individuals (this is where opposites attract comes from).
Our Sun sign is very much our "true" inner self, Moon is our emotional self
What happens all too often, is we meet someone who , by rising sign for that is all we see at first, seems compatible, then after we work our way through that "getting to know you" First house phase, then we get to see what is behind that metaphorical mask, This is when our Sun selfs become exposed..
Our Moon signs , well that is an indication of how we nurture and what we need to FEEL nurtured ( or , loved if you will) is our EMOTIONAL selfs. so yes it is very possible for two incompatible otherwise sun sign people to form strong lunar emotional bonds .
Of course , there are other planets in play, Like Mercury, (communications and thought patterns), Venus (desires) , Mars (Passions) , Jupiter ( personal growth) and Saturn (restraint)
Case in point, My wife is a #Gemini Sun and I am #Virgo Sun (srry about hashtags, Is a twitter habit) by all typical interpretations, incomparable basic personalities. HOWEVER she is a #Taurus rising and I am Virgo rising. Our basic Persona's click and harmonize. Our Moon signs, though, tend to conflict at ties, I am an Aries moon, so express my lunar Love through doing things for her , she expresses her Cancerian "Love" by mothering and nurturing .
Does this shed any light on your question, P.A??