It's been a good while since I saw this movie, it's a difficult watch - you understand.
I think there is a lot of frustration in young men in particular to admit when they were wrong. There is a massive amount of pride that must be swallowed, sometimes followed by shame when you can rationally see when you where wrong, how badly you may have acted and whom you may have hurt.
In this case, it is clear like you said, he didn't agree with his father but it is the only way he was taught. His brother was much angrier and was not able to find another outlet and was captured on video expressing certain views.
While Danny's path was different initially, he was emboldened by Cameron so he and his friend Seth followed along, not because he agrees with the beliefs of Neo-Nazism per se but because as white young men in Los Angeles of the 1990's, the sense of belonging and protection that the group offered was too tempting to resist.
So the tear represents shame, regret, frustration with what could have been if things were different but we can seldom change our circumstances. We can just try to ensure that they don't change our outcomes.