This sort of behaviour by parents in playgrounds makes me really cross; it's as though normal warmth and good manners go out of the window. I'm not surprised you're feeling like you do, OP.
Assuming you've got a few years of this ahead of you, it makes sense to attempt making friends. At infant and junior school, when the DCs' social invitations are controlled by the parents, what sometimes happens is that some parents will only issue invitations to DCs of "preferred parents", without letting their DCs the freedom or choice to see who they want, outside of school. This makes it very lonely for children - and especially lonely for DCs who are "different" in some way, perhaps because of their faith, race, class or disability.
I also think that schools and PTAs should be far more proactive about this, especially in extending the hand of friendship to "new parents" who have just joined the school community.
I was lucky in that when my DS started school, the other parents were in the main, a lovely bunch and we were all in the same boat. Friendships were formed easily, but we all had a policy that as soon as a new child joined the school, we would all invite that DC round for tea and without being pushy, include the new parent instantly, empathising with how difficult it can be as the "new Mum or Dad in the playground".
When my DD started school, the parents in her year group were not as friendly or open as the other group, but what worked in that instance was to open the house to whoever she wanted round and not to get overly concerned when the reciprocal invitations were slow to arrive. Eventually she formed her own friendships with girls who wanted her to visit their houses and it became more of a two-way thing.
A few things might help.
DO go to that meal. Sometimes when parents are "off duty", they loosen up a little and you will see more warmth. Do also disclose how difficult you have found it, making new friends in the area - and how you would value getting to know more people. Some of these parents might be making assumptions about you being aloof or disinterested, when in reality it has been a coping mechanism. A little self-disclosure goes a long way in new relationships.
Keep issuing invitations to whoever your DC want round for tea/play. Remember too, to encourage their friendships with DCs who are "different" and who might be marginalised, but don't force any friendships that aren't wanted.
Look out for the parent in the class who is also sitting in her car/looking lost/playing her I Pod. It's possible that she is feeling just as insecure as you.
At pick-up times from parties/play dates, try to get conversations going with parents who are better when off the school premises. For some people, being in a playground evokes all sorts of memories of their school-days and they are far more natural and warm on neutral or home territory.
Offer to help at PTA events, consider joining this group. Also give some thought to school governance, if you can offer that level of commitment.
Both of mine are at secondary school now and the adult friendships that have lasted and which I treasure, are with parents whom I would have befriended in any other situation, i.e. work, the running club etc. That said, I've made some lovely new female friends through the DCs' secondary school friendships.