The difference in thinking can be boiled down to reformism vs.radicalism. Those who are reformists believe the ideals of the American constitution are good ones, and that the American system of government is adequate for the problems we face. They believe our system of government gives them the tools they need to improve things, so they work within the system. Reformists tend to have more respect for institutions, and to take part in institutional roles. A reformist may never think we're living up to our ideals, but he'll appeal to those ideals in order to get where he wants to go. So he wouldn't see any problem with honoring national symbols while disagreeing with leadership, or with certain policies.
Radicals believe the American constitution is fundamentally corrupt, and that therefore fundamental changes are needed to face the problems radicals see. They don't believe the institutions we've set up can improve things, and they may even think our institutions are intended to oppress certain people. Since they believe the whole system is corrupt, they don't feel any need to respect our institutions, and tend to work outside of established ways of doing things. A radical thinks things are set up against them, and that the only way to get where he wants to go is to challenge and change ideals. A radical sees the problems in their world as being fundamentally connected to their society, so they can't honor the symbols of that society as long as those problems exist.
There are times and places where radicalism or reformism are more appropriate. Americans have tended to be more reformist, hence the long-standing Constitution and the lack of a revolutionary political movement throughout most of its history. But, of course, I think anybody who doesn't want to make an idol of their country needs to be open to the idea that it may have been founded in a corrupt ideology. For better or for worse (I think for the worse), radicalism seems to be increasing in popularity, on both the right (among some on the "alt-right" and among some post-liberal Catholics) and the left (among those influenced by critical theory and radical feminism, which animate the "social justice warriors"). Take a look at the trend in patriotic feeling for evidence of this:
https://www.nationalreview.com/corner/gallup-democrats-drive-u-s-patriotism-plunge/
"Republican national pride has been consistent, Gallup finds. The 76 percent of Republicans who expressed extreme pride in the latest survey is 10 points off the high of 86 percent in 2003. “Even when Barack Obama was in office,” Brenan writes, “Republicans’ extreme pride never fell below 68 percent.”
Fewer Democrats than Republicans have said they had pride in America since the poll question was first asked in 2001. Lately, though, Democratic pride has fallen off a cliff. Just 22 percent of Democrats say they feel extreme pride for their country in the latest survey. That’s half the number recorded prior to the 2016 election. Needless to say, the nature and policies of the forty-fifth president have contributed to the Democratic plunge.
And yet I was also struck by the decline of Democratic “extreme” pride during Barack Obama’s second term. It went from 56 percent in 2013 to 44 percent in 2016. "
