Charities and municipal governments are legal fictions of the states. I do not know the specifics of how these charities are set up. I presume they are ownerless non-profits. (If not, the New Jersey legislature could simply create such an entity type.) Determining common control with municipalities will be tricky.

That they are creatures of the states, and not the federal government, is what will make the lawsuits interesting. The most realistic pathway for the IRS would be to argue these charities do not qualify as such under federal tax law. How they will do this, within the confines of the 10th Amendment and a haphazardly-written tax code, without hitting other charities, will be delicate and complicated.