Anger and sadness are both very helpful, understandable and ok emotions. There is nothing wrong or dysfunctional about either of those feelings.
I think the cultural norm that certain emotions are “bad” and that we can “change” our emotions is extremely destructive for many people.
We can control (and our responsible for) our thoughts and actions.
I don’t think people can actually control their emotions however and making people feel ashamed or unhealthy because of their emotional reactions is unfair. This is actually one of the symptoms of abusive parent-child relationships that I think many people have unavoidably internalized.
A lot of people have experienced serious emotional trauma due to cultural norms and an unhealthy value system about how parents treat their children (as well as by being parented by traumatized people who have grown up in similar circumstances)
There are a lot of good books about it if you search for Complex PTSD. One that I think covers a lot of information holistically is “Healing Developmental Trauma” by Laurence Heller and Aline LaPierre
It's still really tough to know where to go from here. I feel like I've learned from his mistakes, but is the same true for him? Why hasn't he tried to change, is it the society/culture he grew up in? How much is his fault? Still figuring out how to deal with these questions. But I can be angry, and have pity too.
The Fox, the Crow and the Cookie is still one of my favorite songs.
I give them targetted praise whenever they do something I want. Give treats for wrong decisions but drilling what they did was wrong. Make them feel important and special. Let them feel guilty for not being able to live up to the expectations you build around them. Let them see the perfect human you see them as. Use metrics and numbers that are easy to parse, use social signaling. Instead of giving your opinion about something, point towards someone they might be interested to hear about or care to change them.
Say you love them the way they are but point towards changing societal expectations.
Again, you aren't the bad guy who wants them to change. It's the society or someone else. It is easier to get through the head.
Push them into groups with opposite view to them. People behave differently under group pressure compared to when you are talking to them one on one.
Whenever they come across material that re-enforces their existing belief, try to distract them. Change their environment. Offer to clean their room and remove harmful material. Change places that remind them of their previously held beliefs.
Not everything that works for oneself will "vastly improve" the lives of others.