The question in the title is a reference to the myth that the famous Maine Coon cat is named after a domestic cat x raccoon hybrid offspring in the 19th century when a domestic cat mate with a wandering and horny raccoon. Some people still believe and say that a raccoon can mate with a domestic cat. It is a conspiracy theory which is still doing the circuits on the internet.
I have two points to make on this. Firstly the origin of the name “Maine Coon” may be an indirect reference to a supposed cat x raccoon hybridisation. However, my assessment is that the name is a reference to a certain Captain Charles Coon who plied his trade on the east coast of America, specifically New England. He loved cats and some were long-haired. You can read my full discourse on this by clicking on this link. However, Captain Coon may be a fiction (his name sounds unreal and too convenient) but his name may be the source of the “Coon” in Maine Coon!
Secondly the best authority on cat genetics, Sarah Hartwell, states that a raccoon x cat hybrid is genetically impossible (see quote above from her messybeast.com website). This is why there are no raccoon/cat hybrids in existence nothwithstanding the people would love one to exist.
This is genetically impossible. However, impressionable (or merely stupid) individuals have attempted to mate cats with raccoons.
The narrative that domestic cats can mate with raccoons is a bit of a myth like big cat sightings in Devon in the UK where there are no big cats. People want to believe these exotic stories to brigthen up their lives. Breeders can also disseminate stories about their breed if it helps to sell cats.
My conclusion is that cats don’t mate with raccoons and if they do no offspring are created. Raccoons can attack and kill cats but sometimes they can friendly with cats when socialised to them.