I have the same problem! Even a dog who likes the "get the cat" game.
Hubby is VERY allergic to cats...we have medical bills to prove it.

We have a MAJOR problem w/ people not keeping their cats up...yes it's a no-no where I live, but no one has ever enforced it, so...
I tried asking the owners, who all took turns with the claim, "well, my cat doesn't leave my yard or EVER get on cars, it must be theirs."
Then when I got no help from them, I invested in a live animal trap (less expensive than med bills!) and started catching kitties. After about the 3rd one had to be retrieved from the no-kill cat shelter 20 miles away, they became indoor kitties.