As a guy who has a race car sitting in his hangar, I see both sides, somewhat.
Firstly, airplanes should have the right-of-way at airports. While track days are always pure recreation, airplane flights are often business/medical necessities.
The exception- My local airport has large, mostly vacant tie down area that has a bunch of orange traffic cones set up a few times a year where local law enforcement holds their advanced driver training. They use a back gate, do not cross any active taxiways or runways.
On the other hand, sports car clubs are always desperately seeking more track days. Having been a member of multiple car clubs, I've seen pleasant negotiations, combined events where a couple clubs share a track day, and I've also seen clubs DEMAND another club give up some of their scheduled days to make it "fair".
There is plenty of overlap between the airplane crowd and motorsports enthusiasts. When I started racing, I was surprised to find out how many other driver's are also pilots.
While every situation has its own peculiarities, as a general rule, airplanes have the right-of-way at airports, but I'm happy to occasionally squeeze flying over to one side a bit and make room for the car guys. Large slabs of flat pavement are rare. If we can share some, why not? It also brings people with discretionary income onto the airport property, where just maybe a few will think those guys flying look like their having fun, and perhaps wander into the FBO and inquire about lessons.
Also- guys & gals who have gone through the training to get a competition license are NOT the idiots on public roads. After you've gone through Turn 1 at 140 mph, it's no thrill to do 80-90 on public roads. After burning through a pile of adrenaline on the track, one tends to drive very conservatively. After all- there is no longer anybody waving a big yellow flag if there is danger ahead. The track is a very controlled, safe environment, and, like aviation, attracts high-quality people.