I don't want to be touched randomly in public by a stranger, and I wouldn't want it for my kid either. Obvious exceptions are emergencies, kid is lost, etc. If a kid approaches an adult and passes them a ball or etc, you expect some interaction, but if a random adult started hugging my child or stroking their back I'd find it odd.
There is just no real need to be touching strangers, and that includes children. Babies are a little different as they're typically being held by a parent, and most people want to stroke their cheek or whatever. I don't mind this, as long as people ask first. I have 0 issues with men smiling at and waving at my kid from a distance either. I'm more than happy with interaction, just not touch.
But anyway. Frankly a lot of men are predators, and commit the vast majority of sexual crimes. If men want society to treat their interactions with women and children with less suspicion, the onus is on men to do better.
And no, I wouldn't feel the same about another woman, because the likelihood of another lone mother in a park being a predator is exceptionally low.