Is it fair to say that Captain America would be extremely concerned about Americans kneeling for the national anthem – but he’d be concerned about there being an issue serious enough for such a protest, not the protest itself?

Captain America was around for the protests of the 1960s, and sided with the protesters when it came to radical occupations of univerisites, so he’s absolutely going to back someone in a peaceful symbolic protest. In fact, he’s explicitly made the same kind of arguments that Colin Kaepernick is making:

And as I’ll discuss in a forthcoming People’s History of the Marvel Universe, Captain America has specifically dealt with issues of police brutality before. Starting in Captain America #139 (1968), Steve Rogers joined the NYPD, where he championed community policing, fought police corruption, ended urban riots peacefully, and brought down the Cowled Commander, a supervillain cop working to fight reform of the NYPD.

So there is no doubt whatsoever in my mind of which side Cap would be on.