If your insurance company finds out you are dragracing, you might be canceled. I had State Farm for 30 years and they longer wanted to insure this car once they found out. I then had Allstate and even though car was never to be street driven again (modded beyond street use), they were about to cancel.
Even if you are 100% stock, your insurance company will likely not be happy if they know the car is raced (location irrelevant). Once you become heavily modded (like mine), it can become a major problem and uninsurable, to the extent that I turned the license plate into DMV a few weeks ago. Not insured....not required to be insured....racecar use only. As far as being insured at the track, for one car as a private individual, the only insurance I have found (that is realistically affordable) is insurance at the track while parked, stored, being transported via trailer etc, but nothing while actually racing.