My parents and DH's parents (all passed now,) rarely met to be honest, despite only living 6 miles apart.. They met about half a dozen times. Mostly at family things (Weddings/ Christenings etc.) They didn't 'not' get on, it was like many people have mentioned on here; they just didn't have any reason to get together as they didn't know each other.
The women were SAHM's and couldn't drive, so 6 miles away, may as well have been 36 miles. And the men worked full time and would just meet the neighbours at the pub a few times a week. None of the parents ever socialised (with each other,) or had any desire to.
Me and DH however, have had a bit more contact with our (young adult) children's partners parents. Our children have left home now but when they started dating, none of them (children OR their partners) could drive. So we would give them lifts, and their partners parents would sometimes too, so we would occasionally say hello and chat for a few minutes, when we dropped the kids off.
The adult children can all drive now, but we still see the other parents maybe once every 6 weeks or so for a few minutes. They live only a few miles away, and we occasionally see them in the big shopping centre, and stop and pass the time of day for a few minutes (like you would with a neighbour.)
I think it's probably a bit more unusual now for people to not meet or have any contact with their (adult) child's partner's parents, as people communicate more via social media, women work more, and women drive more, and 6 miles away is nothing these days. But I guess it still happens.
Our kids say they would find it very weird if we didn't have any communication with their partner's parents. That said, although we see them maybe once every 6 weeks, and pass the time of day for 5 minutes, I don't particularly want to socialise with them. One of the mums of one of our adult child's partner's, has said recently 'your parents will have to come for a meal sometime.'
I'd rather not to be honest.
She means well, and she is a nice lady, but I don't want to socialise - and neither does DH. He said 'they are pleasant people, but make any excuse you can to not go.' Sounds awful, but we just don't want to. 