The only thing you really have in common with these people is that you have children of a similar age - that's it. You wouldn't expect all your work colleagues to automatically be your friends just because you happen to work with them.
I don't really understand this argument, and don't think it's helpful.
The OP doesn't expect all the Mums to automatically be her friend.
But when you get thrown into any group situation, you expect and/or hope to make friends with some of them.
I don't expect to be friends with all my work colleagues, but over time I click with some and make friends with them. Same as when I was at school myself, University, etc.
The school gate is no different. You're thrown together with a group of disparate people for an specific reason.
Most you won't even pass the day with, some you will get to know and some you'd expect to make friends with, the same as any group you're thrown into, in life.
I'm sorry you're experiencing this, OP. It's so unkind to post pictures on social media, when you know there will be people looking in from the outside. I've long since stopped posting and sharing, because I actually think it's kind of ... I don't even know how to express it without offending people. But a definite part of it for me is 'how would this [photo of group of people having fun] make someone not included feel?' And the thing is, there will always be some people not included, and it's very, very rarely for unkind reasons. It's just because you can't always invite everyone. That doesn't make it any easier for the 'excluded' person, though.
It's difficult, once a group forms, for others to infiltrate it, as it were. It shouldn't be, but it is, especially if you're shy, reserved, quiet, etc.
I think all you can do is keep inviting friends over for your DS to play with, and try to keep the focus on him.
