I wouldn’t think this is weird as they are more than likely believing that they will meet your son someday while with your mom. If this is a problem for you then I would start discussing your boundaries with her now rather than later.
My husband's grandma is the same. Her gross behavior on social media actually made me sure that I was done with it! No more FB for me, i don't need that weird attention! I guess some people do though 🤷♀️
It is weird and completely out of line for the grandparent to not correct people. My grandmother wanted to post a pic of my baby but decided against it when I said I am keeping it on the down low because my ex is denying paternity. Your mom is way over stepping and needs to be told you’re not comfortable with your baby meeting people you don’t even know. If there is any pushback from her then it’s supervised time and she wouldn’t be left alone with the baby if it was me.
No this is actually weird. I would tell your mom how you feel and set boundaries. Overstepping parents are the worst