They have Free Speech rights on their dime. But while they are “on the clock”, working for their employer, they abide by their bosses’ wishes and their written contracts. End of.
It is more than a little troubling to me that many people see today's temper tantrum in Free Speech terms -- going so far as saying NFL players don't have Free Speech rights. Today's incidents had nothing to do with Free Speech one way or the other since the government wasn't involved.