I was my wife's caregiver and dad to 5 young sons over 20years. I was the sole parent taking them to playgrounds and other outdoor activities, upwards to 200x a year.
In all those events, I never experienced nor witnessed anything remotely like what you described. Not for me and not for any other solo dad. On rare occasion, I was complimented for spending time with them. That's about all the notice I got.