Myths about compatibility are common and damaging. You don't have to be compatible to live happily together, but you do need tolerance.
Just because a problem has been around a long time that doesn't mean it'll take a long time to fix. We seem to believe in a sort of natural law which says that if a problem has been around for a long time, it will take a long time to fix. But there is no proof of this beyond our own beliefs. If we can free ourselves of this self-limiting idea, rapid change is possible.