Is it illegal to register or insure a car that originally had an airbag but does not have one anymore if you do not want to repair it?

Probably. Remember, there are still plenty of cars on the road that don't have airbags. And, of course, you can switch airbags off on a lot of cars these days.

You don't mention it, but often when the airbags in a car go off, the car might be considered a total loss. If that's the case, you might have difficulties in getting insurance back on the car if you're not planning on repairing the vehicle. You might also have issues with the state, which could require you to make the vehicle road-worthy prior to registering or paying for your yearly tags. This could require some repairs, and the state inspector might not "pass" the vehicle if the airbags don't work.

Sounds like you've got a lot of footwork to do, but start with your DMV first and go from there.