Only members of your project can see the location of traps and bait stations, and even then they will only see their own stations or those assigned to them unless they have an elevated role (readonly, editor, administrator).
If you list your project publicly people outside your project will only see your project boundary on the map. And if you opt in to sharing summary data, your catches will only show up as statistics with aggregate approximate locations (generally as honeycomb hexagons or heat maps) which aren’t useful for anyone trying to find the specific location of an installation.