Football stadiums get subsidized because football is extraordinarily, wildly popular with most of the people that pay taxes. Those taxpayers spend massive sums of money on sports every year, across the NFL / MLB / NBA / NHL / MLS / NCAA. Those people pay most of the taxes that fund the government that then pays for the stadium subsidies.
Taxpayers love sports, love spending money on sports, and the majority of taxpayers are clearly fine with subsidizing sports at all levels. They vote with their dollars and... votes, over and over again, year after year, decade after decade, to keep supporting sports subsidization.
See: football attendance and ticket spending on NFL and college games annually, as well as sports packages for television, merchandise sales, etc.