It seems to me that you are confusing patriotism for righteousness. Standing up for what is right isn't synonymous with patriotism, in fact the actions of nation states is often quite opposed to righteousness.
In the US, we have a federal government that engages in all kinds of immoral activity. It steals, it has unjust money, it fails to provide an adequate justice system, it fails to take care of the poor... Have you ever read the Old Testament? How many times is Israel chastised for failing to take care of the poor and not enforcing justice?
Also complicating the issue is the fact that there are many different ideas about what is right, wrong, and American. What if you were stoked about the way things were going under Democrat rule, but hate the way things are going now? Are you supposed to cheer lead policies you oppose?
This idea that the US is somehow a special Christian nation is laughable. Sure, some of the founding fathers were Christian, but most weren't, and they intentionally built a secular government. It was a wise thing to do. But to say the nation has always acted Christian is to completely gloss over the brutal violence that has been a hallmark of establishing and maintaining this country. Every problem the US has is solved with violence, or threat of violence.
How could a Jesus follower get behind an organization like that? If you want to be patriotic, then you can patriotically support your true country, The Kingdom of God.
By the way, your quotation from Psalms isn't a blanket statement saying that any nation who is mostly Christian will be blessed. The passage is specifically referring to the ancient Israelites. The LORD chose Israel as his heritage, and the "nations" are the people God did not chose. See Deut 32:8-9.