Try giving the cat something high and defensible to lay on that is on the side of your house facing the neighbor’s house. Cats like cars because they are high, with no obstructions, easy to defend, and the metal is comfortable at night.
I have a car he is perfectly welcome to lie on as much as he wants to. But no, he wants to get on the neighbor's cars.
As for neighbor; he is right about the tarps; but only if left on; and not removed for long periods.
That said; if he really VALUES his car/investment; he should protect it by storing car, PROPERLY; as do those who share same love of antique cars and actually appreciate their value and so insure proper protection by way of safe storage. What is HIS problem?
Surely; your cat is not the only threat/risk to this cars value. Elements, Et Al; are major considerations; for an 'outside' antique. Not to mention 'other things'. . .So he is inviting 'reasonable risk' by leaving antique outside; and without protection.
Consult a lawyer on 'what is right'/legal and reasonable expectation per law.