Yeaahh, you can achieve a certain amount with 'be kind, or people won't want to play with you' but actually, not that much. I've done a fair bit of that and, with an angry or frustrated child, it just sounds like a threat, or a put-down.
Children, even the most empathetic-seeming, sensitive ones, are massive ego-maniacs. They're often seeing themselves in the situations the appear to be empathising with, rather than actually caring about the fictional character, or other person.
Children, like adults, would almost all agree that bullying is wrong and will be quick to tell you when other people are being bullies, or unkind. They are the heroes of their own story though, so find it very, very hard to identify objectively when their own behaviour is unkind or bullying. To them, it's always because something external was unfair and they were reacting to that.
They are not perfectly rational and, in the midst of a strop or a tantrum, completely impermeable to reason.
Also, like all of us, they believe the evidence of their own experience. Unless a playdate has actually been cut short because of their behaviour, or a friend told them they're not their friend any more for this reason, they won't believe you.
I've told my DC there are things we haven't been able to do, invitations I've declined, more often things never planned or considered, because I knew it would all go wrong, behaviourally, and be unpleasant for the us and other people (e.g. terrible loser, so meeting to play board games just wouldn't have been fun). Examples are demanded. Of course it's hard to remember specific examples of things we didn't do! It is essential to be able to illustrate the point though. And actually, you do need examples of times it did go wrong, otherwise it's just about your belief (and they'll say 'I can behave well if I want to, I would have been fine'), not their behaviour. You need to be able to say 'you said you'd behave well that time but you didn't, so and so was upset / you damaged X, and we had a to leave'. Then... move on to discuss the tactics they're going to use to avoid that happening again.
You need your child to be able to talk to you about friendships, relatioships, other people. If you say 'other people won't want to play with you' and always make it sound like your child is the problem, they won't talk to you about the times other DC were unkind to them, because they won't expect to be believed, since they think you've cast them as 'bad, antisocial child'.
I find that rational explanations at calm times do sink in and are believed. They can then influence behaviour in the moment. But, often in the moment, the feelings experienced are too powerful for rationality or memory to come into play.
So you have to have straightforward commands and consequences too.