I'd say most people don't like players protesting during the anthem because the NFL made it a pseudo-salute to service military ceremony. Some folks find it distasteful to take the attention away from that and draw it to other things. They don't want these players to never be activists or to never speak out, just that they find a proper time and place to do so. I'd say, from my experience, that's how a huge chunk of the "!@#$ Kaep" crowd feels.
Rightly or wrongly, the anthem had become ingrained in football and our American culture had conjoined it with patriotism and supporting the troops. You saw it way back in the first Bills Super Bowl with the show of force during the anthem. It was a symbol of America and our military.
I don't think they should "do away," with the anthem. This saga sucks on all sides, but the anthem is football. Far too often we call our football players warriors and preach about their sense of leadership, toughness and devotion when the true warriors get less attention. Remembering who are the real heroes is important. Maybe not to some soulless parasitic leeches, but it's important to the heart of America.