I used to take my kids to the park a lot (worked from home, gave my wife a break). I never thought it with my own kids, but sometimes the other children (strangers) at the park would join in and I felt a bit awkward. I'd ask their mom's if it was okay. (Hide and go seek, catching my kids as they jumped off the monkey bars, etc.)
It made me feel mad too that I had to even think that way to be cautious of what others thought.