I forced one of mine to invite a kid who was bloody awful to her because there were only ten girls in the class and it was the right thing to do. That bit me in the bum when a few months later she asked all 8 girls and missed out DD telling her she was C-list. That was primary school.
This year in secondary I find myself having similar problems...
Me: you hang out with a b c d now, but e f g h asked you to theirs so you have to ask them back, it's reciprocal, it's fair. That leaves i j k l ... you sit next to i in science, she'll be upset. j didn't ask you to theirs so probably won't be that fussed. But that means two have been missed out. Is that not unfair?
Her: Shan't bother having a party then.
Pupil k has emotional and behavioural issues. This has included threatening to cut DD with a knife, calling her fat and ugly and trying to hit her. These are teenagers so asking a parent to stay at the cinema/pizza place is just weird, plus k's mum not approachable (have met her twice).
It is a bloody minefield.
Out my three, one is not that popular, one is somewhat boisterous. They have had to accept that they are only responsible for their actions, not the actions of others, and sometimes life just ain't fair.
Did my third have a party? Yes, and discreetly gave out invites to most of the girls, but knowing some could not make that date they did not get invites (so it looked fairer than it actually was). Did I force her to ask k? No, I didn't.
The knife threat did it for me.
Plus my kid has to put up with boisterous (undiagnosed) younger sibling on a daily basis. So her sister did not go either.
Genuine rather than goady question to parents of children with individual differences...
If your class had a gender divide which was small. If your child only wanted friends of their own gender. If one of this small divide had been causing your child grief for a whole year because of their differences: would you still invite them?
(you cannot say pick the other gender as child doesn't want to, you can't say pick fewer kids as the ones you are asking might not come anyway and it's only a third of the class, you can't pick kids outside of class as there aren't any to ask...
so given the one not being asked becomes the only one in that gender split not going BUT has made life hell for your child because of his/her SN...what then?)