create open map where people can add themselves by state/department

I’m thinking of creating a map addressed to a community on which people can add themselves by state, region or department (based on their preference). Of course not give away their precise address or coordinates as the map would be open to the public.
Has this ever been done or does one have an idea on how I could go about it?
Note that I’m a noob on creating a custom map.

Can you indicate which custom map service you are using, as OSM itself only maintains one map, which is fully public.

I’m not using any service. I’m actually looking for the best suited one for this task. Though I want it to be based on OSM, like Umap or the like.
What would be awesome is if people could check a box to select between Country, Region or Department and then just click on one in the map (or in the search panel) to add themselves to it.
But what really matters is that the map should prevent users from entering a precise address.
I’m hoping someone already did a similar thing to make it easier for me.