The very short answer is that cars work perfectly well around wizards.
Quoting from Pottermore's page on "Technology" (as written by JKR herself)
There is one major exception to the general magical aversion to Muggle technology, and that is the car (and, to a lesser extent, motorbikes and trains). Prior to the introduction of the International Statute of Secrecy, wizards and Muggles used the same kind of everyday transport: horse-drawn carts and sailing ships among them. The magical community was forced to abandon horse-drawn vehicles when they became glaringly outmoded.
It is pointless to deny that wizardkind looked with great envy upon the speedy and comfortable automobiles that began filling the roads in the twentieth century, and eventually even the Ministry of Magic bought a fleet of cars, modifying them with various useful charms and enjoying them very much indeed. Many wizards love cars with a child-like passion, and there have been cases of pure-bloods who claim never to touch a Muggle artefact, and yet are discovered to have a flying Rolls Royce in their garage. However, the most extreme anti-Muggles eschew all motorised transport; Sirius Black's love of motorbikes incensed his hard-line parents.