I think this is a good start. The dilemma I see is that those who believed in the standards of the Confederate States of America can have integrity, but I would dispute this due to their inhumane beliefs, racism, and inability to understand that other classes of people are owed dignity. So a confederate might have integrity within their own ideological standards, but in the broader sense they have very little.
Most of those who identify as Confederate would also identify as Christian, which (when compared with their actions and words) would cause their integrity to fall apart rather quickly.
They also tend to identify with the Antebellum U.S., including the Declaration of Independence, which states "all men are created equal." Anyone with eyes and ears could have seen they were lying about that. Even after the Civil War, the 14th Amendment supposedly guaranteed equality, but they embraced separate but equal which, in fact, was not equal.
So, I would still stand by what I said, since they are/were clearly
not following their own standards and stated principles. Their lack of integrity is easily exposed when pointing out these obvious discrepancies and inconsistencies.
So I suggest principles need to be liberal and tolerant, and not assume a sort of superiority of self, so humility is crucial to integrity. This would render a person who believes in any sort of strong ideology as having limited integrity. I say this because we often see those with a strong ideology valuing their beliefs over humans, which means their moral sense is set aside for what the ideology says. It's a complex issue.
Few people would ever openly or publicly declare support of murder, theft, racism, corruption, or any of the so-called "dark triad" traits which could be reasonably considered bad or malignant principles. Fewer of them would get elected to public office on some kind platform openly endorsing evil and malice towards other humans. Even the worst of villains will always tend to try to pass themselves off as "good," one way or the other.
On the other hand, looking back, there may have been some principles which most today have identified as malignant and racist, yet people back in the 19th century might not have seen it that way due to having different values, beliefs, and standards. So, you're right, it is rather complex.
And I do agree that principles should be, on the whole, liberal, tolerant, and other qualities most often identified with "good." But if someone wants to embrace evil or dark principles, then I would say those who are honest about it would have more integrity (in my opinion) than those who are not.