Many media people live in the area where I live so I have encountered many actors, comedians and tv journalists over the years. I wouldn't want to intrude on their private life, and nor do the vast majority of others, so if required to speak to any, I act just as I would with any other person I do not know. Otherwise I walk past as if I haven't noticed. I imagine that's what most celebrities would prefer.
The only one I recall being rude was a very well known ex member of the Eastenders cast. I don't blame them though. I was at a hotel on a work conference and one of my colleagues saw them at the bar. She is really pushy and insisted on questioning this person about their role in the soap when they clearly wanted a quiet drink. They have since been actively involved in fund raising for the local secondary school one of my DC went to, where their child also attends.
The only one I passed slight judgement on was a tv journalist who has since had a meteoric rise. I saw them a few times at the local playground with their kids who are similar in age to one of mine. At the time the kids were very young (under 5) and this person paid them no attention at all, always being glued to their phone, making what seemed to be work related calls.
As for the OP. I'm sure there any many other parents in the playground who would like an offer of friendship. Plus nice friendly groups of mums can be daunting for many of us. I was treated kindly by many people in the "group" at my DC's primary school, and did socialise with them at times, but the close connection of some, the reason for which was never entirely clear to me as kids were in different years etc, always felt intimidating. I was not sure who liked who or how well they knew each other, so always felt 'other'.