Does every state in the US require aircraft and pilot registration?
No.

It varies from state to state. New York, for example, requires tax payment but no aircraft or pilot registration. New Jersey doesn't require any registration and didn't mention any taxes. In Delaware, registration is required but taxes can be waived if you register your aircraft under your corporate, instead of your own name. Iowa requires registration and so does Ohio.

I could not find a single resource which lists all states and their aircraft and pilot registration requirements. FAA does not have this information, probably because FAA does not care about state regulations.

We can create a Wiki on this topic here.