Does Cork not have a football team?
They do. They are the current League Of Ireland champions. They are the best supported team in the country by a mile. They are run by a supporters trust having (once again) been run into the ground about 8 years ago through financilal mismanagement and a proper Walter Mitty at the helm. Kevin Doyle and Shane Long are 2 players who left Cork for the english leagues in the last decade.
When I was a youngster in the 70's, in Cork, i went every week to see my team, Cork Hibernians or the other city team, Cork Celtic play. It was an amazing time to be brought into footie. Hibs were a great side and played in the European Cup. once against one of our favourite german clubs BMG.
Anyway the point of this ramble is Hibs went bust, Celtic went bust, Albert Rovers their next incarnation also went bust. Cork United and Three Rock Rovers, Evergreen Utd all preceeded Hibs and all went bust. Cork City are around over 20 years and are now, finally, stable and flourishing. It's a fun place to go watch a game.
So, Cork has a soccer team (as well as Hurling and Football-GAA) and Rugby (local and provincial, Munster second home). All my mates who go with their kids to watch Cork City have english clubs they follow as well, it's just the way it is.
As such everyone who loved soccer down in Cork adopted an english club as we could never hang on to any of our own, That is why, down here there is such a strong Reds following (and Utd etc.).