Since I was a Giants fan, I never went to the Stadium to see the Yanks play. But the football Giants played at the Stadium. And in the early Sixties, before the bleacher seats went to reserved status, you could still show up and buy a ticket at the gate. I went to plenty of football Giants games. Sitting in the bleachers was a real trip. Even then it was incredibly rowdy. The band played in the bleachers. Half the people were drunk. When the other side scored, and the band played their themesong, bottles would rain down on the band--often missing and hitting others. Lotta people wore football helmets in the bleachers, and believe me, they weren't players on the sidelines.
If memory serves, there was a football Yankees team in the early Fifties--and they played at the Polo Grounds.