No, race-car insurance isn’t compulsory. But it makes sense to have it in case not everything goes to plan. Circuits have challenging twists and turns and accidents can happen, so you might find track insurance beneficial, especially if you’re new to track driving. Even if you’re a seasoned circuit-goer, you’re not infallible.
In any case, the car club or organisation running the track day might insist you take out extra insurance.