The NFL and other major sports organizations should definitely not be tax-exempt. Tax-exempt status is usually reserved for non-profit organizations. The NFL makes more money than God! Seriously, they make so much money off of the players and the memorabilia they put out. They are also not a charitable organization, so there is no reason they should be tax-exempt.
Sports organizations should not be tax exempt. It is a huge money making market that is no different from any other entertainment that makes a profit. It is not a religious or charity organization, and as such, should be required to pay taxes just like any other entertainment organization. The players and teams and the NFL make huge sums of money.