I own my tank. I have a billing dispute with my supplier and they threatened to shutoff my tank. Can they do this legally, if I am the owner of the tank?

Where, and are they citing safety issues?

Why are they shutting off the tank? To somehow force you to pay for the propane.

Tell them they cannot enter upon your property or they will be charged with trespass and (if they shut the tank off) criminal mischief.

Of course, good luck trying to find another propane supplier.

You may have signed a contract allowing them access to the tank and also the right to withdraw propane that is not paid for. What does it say?
If you have a dispute over the bill, get to small claims ASAP.

The issue is that unless you paid for it, they own the gas in the tank.

What they can or can't do will be in the contract for the services