You probably can get away with having your cat at the park. I don’t know how leash laws work in your hometown but I know some towns require that they be on a leash. So that is a possibility
When I was in highschool and I had to walk to my bus stop, all my cats would follow me so everybody laughed and made fun of me. I had to walk them back homeI actually made a few friends that way.
I have cats follow me all the time too. I've befriended a lot of my neighbors because of their cats, even people who don't live by me.
But I always stop whenever I'm out (but not driving) every time I see a cat, to see if I can get them to come up to me. Eventually I wind up making a lot of friends, feline or otherwise.
This is generally what they do:
And yes, this is actually my video. I took it one summer day of one of the cats that led to a friendship between my neighbors.