I am planning a visit tentatively for Feb 24th. Should there be a government shut down does the space centre remain open or does it close? Thank you.

Open. It is not run by NASA or other fed agency. It is not funded with any taxpayer dollars.

9:00 AM to 6:00PM. CHECK THE NEW ENTRANCE

See on their homepage https://www.kennedyspacecenter.com/info/hours-of-operation

Open

As far as know it well be open. Have a great time.