Most Americans, including Mob guys, find celebrities and others who lead public lives fascinating, attractive, glamorous, rich and powerful, etc. For that matter, many Americans find Mob guys, especially those often in the news, fascinating, attractive, glamorous, rich and powerful, etc. Entertainers and politicians often cross paths with gangsters because of OC's involvement in movies, music, TV, lobbies, PACs, unions, etc. Sinatra was popular with Mafiosi for the reasons Jace and others said. It was a two-way street: Sinatra fancied himself a "tough guy," and liked to be around Mob guys.
Here's a link to an article that's relevant:
https://www.ranker.com/list/celebrities-with-alleged-ties-to-the-mafia/josh-heller