I think I would find it a bit weird if uninvited there were mums hanging around every week. Especially if my kids started pestering me to come too, I find it hard enough to attend all the school events we are actually supposed to.
But our school doesn't going swimming till they are in the juniors, so hanging around parents would probably be declared 'embarassing' anyway and they currently walk to a local private school and use their pool so I doubt anyone would be allpowed in anyway.
It would never cross my mind to go and watch. My DS had lessons in reception and none of us went, apart from a few SAHM who were good enough to help with changing. If I had concerns about the school keeping them safe then I'd change schools.
But then I am as far from a Klingon parent as you can get.
I was a parent helper...school always desperate for parents as they needed bods for the coach and getting swimming hats on. We weren't expected to actually help take the class. I did get very miffed when there was a gaggle of mums happy to pitch up to watch their kids but would never offer to be on the swimming coach rota.