I like the 'We're colleagues' approach. Some people in that analogy though, see themselves as the bosses...
Here's my experience at a small school:
Over the years I've pieced together that the mums in my school (and dads, but at a distance) sort themselves into a parent hierarchy where at the top are alumni of the school, old village families, local big names (if not alumni) and people of similar social standing with the right face.
They favour their kids being friends with each other above outgroup kids, and parties have been decided along parent friendships as opposed to 'in schooltime' friendships, as mentioned by other posters from reception onwards.
This hierarchy often weaves it's way through all class years and the parents themselves are often related by blood or marriage to each other.
Consequently, at school representive level - on PTA board, as class rep, on commitees spanning church and school, it is the same families seeking and getting roles in same, with the added negative that if you want to serve and do get your nomination under the wire, you will always be serving alongside one of them.
It's become obvious since WhatsApp came along, that class rep roles were nominally open for 10 minutes for 'all' but in reality the reps already knew they were 'volunteering' publicly as it had been sorted in other conversations.
IMO, our school is more clique-ish than many I read about here.
I wish friendships were child-led, but I'm counting the years until Secondary.