They do not need anyone's permission to build the mosque. It is not "in the shadow" of the nonexistent WTC, nor will it ever be in the shadow of anything that they eventually build on that site.
One issue is whether they have the right to build their mosque or whatever it is on the property they own. They do, and no matter who is elected to whatever political office, this will not change.
The other issue is whether it is a good idea to build this at the present time. You can agree or disagree on this, but it will not change the legal right to build.
There is no legal "problem" to solve.