How can relationship compatibility not be important? It is key to a successful relationship. You don’t have to be totally similar or alike in many ways even, but you do have to be compatible even if the ways you are opposite and different complement each other. It is important because relationships take work and to be able to work together as a team in a relationship you have to be compatible with one another. You have to be able to at least solve problems and come up with solutions together, being able to agree on a path to get there.
You have to hold the same belief system, values and morals. You can make allowances for other personality differences like one who is an extrovert and one n introvert, or if one is physically active and one is a bookworm. But you are in trouble if one thinks that cheating on your taxes is acceptable and the other does not, for example. Or if one spouse thinks that flirting with others is harmless but the spouse does not think so.