I'm not sure I'm completely getting where you are going here. Dense moment ? (I have those)
But trying to use your analogy - would it be correct to substitute the word "interest" instead of "compatibility" ? Or is that changing what you're trying to say too much ? Something about the word 'compatibility' - to me - implies too much of a go/no go imperative.
Because if we can do the substitution - where is the conflict or concern ?
Different people have different likes, tastes etc, some we share with others, some we don't. No inherent conflict there is there ?
We cum together on the things we do share and out of common courtesy & respect, allow the space for each other to indulge in the things we don't separately.
So except for examples like you offered where one or the other starts to exert some form of control drama or the different 'likes' are so adverse to one or the other to actually diminish respect - and therefore any shared connection, I think we have to respect each individual's right to seek their own happiness & fulfillment.
Is that maybe a big part of the definition of 'open mind' and even 'love' ? Embracing both our similarities as well as our 'differences' ?
Hope I guessed at what you were trying to get at ?