For a gun forum, we sure seem to have an abundance of Constitutional law scholars...
Does a community have the
right power to tell some one what they can own or not own?
The short answer to the question is
generally, yes. Government organizations (at all levels, but especially local) tell people what they can and cannot own or do all the time. You want to erect (pun intended) a 100' tall penis statute in your front yard? The city will probably make you take it down. You want to make a DIY bomb factory in your garage? All sorts of people will tell you that's not okay. You want to start a free range rattlesnake farm next to a preschool? The gov't is probably going to tell you that you can't own that (at least not in that location).
At a very rough conceptual level, the government can exercise its police power granted to it by the people through the democratic process to make you do or not do all sorts of stuff. The limits on this police power are (1) Constitutional rights and (2) the democratic process. The government can't take away your rights to free speech or lock you up without reason because those are protected Constitutional rights. For pretty much everything else, if people don't like what the government is doing, they can use the democratic process to address the issue.
Now, as to the questions of what is actually a protected constitutional right and how well the democratic process actually works...