1. It's supposed to be inconvenient. Protests don't all happen on weekend mornings with permits submitted. Not just because that costs money and requires time and attention, but, because even for me, who lives in a hometown where everybody comes to protest, it's all too easy to ignore that. Those gatherings are still valuable, I'm not suggesting that the March on Washington, for example, was a waste of time, but those often bring attention primarily to those already committed. So joining hands and getting arrested, or blocking roads during rush hour are tactics often employed because they make news and therefore draw attention of those not necessarily already paying attention.
2. The idea that protesting the death of people is inappropriate during a tribute to the death of people, well, I'm not sure that's good logic at all there.
3. But, actually the national anthem isn't a tribute to fallen soldiers anything more than anything else is.
4. We stand to salute the flag not the song. I bring this up because people keep saying while that song is playing which indicates that people don't even fully understand the tradition they are objecting to having altered.
5. We have developed a tradition of playing anthems at sports games. It is not because sports have anything actually to do with patriotism (except possibly during the Olympics).
6. It's a clever marketing scheme by the military. There's a reason there's always a color guard there. So, it is essentially an ad. You are objecting to the interruption of an ad.
7. You are of course free to stop watching sports. You are free to object to people protesting in the middle of your entertainment. But when you try to claim the moral high ground for leaving, well, check that that horse has legs.