As I noted our religious freedoms are restricted by the courts. Can you erect a cross on government ground? Can you lead a prayer in public school? The first amendment gives unlimited freedom - however the courts restricted it to beliefs, not practices.
This is up for debate and also many Christmas Trees, Menorahs and Creches are erected each year on public land.
Can you lead a prayer in public school?
Up until the 60s you could and it was done in the Founder's times as well. This is a recent atheistic occurrence.
The first amendment gives unlimited freedom - however the courts restricted it to beliefs, not practices
Can a child drink communion wine if that child is below the legal limit to drink alcohol? Yes because the child is expressing his beliefs.
It’s quite a stretch to attempt to include the building of a place of worship as a practice that should or could be restricted. Your poor analogies of erecting symbols on public property fail, when the direct analogies of building a church or synagogue on private property are available.
Personally, I recognize the mosque for what it is, a taunt. However, I also recognize that no has the right to not be offended. When you have freedom, you’ll have offense. Freedom to not offend, isn’t really freedom at all.