It is interlinked. The day we tell the real truth of Karbala is the day we start dismantling and countering this brainwashing. And that truth happens to hurt not the minority but the majority as well.
The Karbala situation, like the situation with Uthman and Ali, were not black and white on a community level. Shia's like to make it seem like descendants of Mohammed had one agenda and Sahaba had one agenda which wasn't true in all those cases. Descendants of Mohammed and Sahaba did not all share same positions and were split on some matters. And not all descendants of Mohammed or Sahaba were really good people. Shia seem to think majority of humans can be like Prophet's which is not true for descendants of Mohammed or Sahaba. We believe first generation of Muslims are best generation of Muslims. And some of these problems involved second generation and so on. We do not believe ordinary humans are greatest Muslims, and that's why we look up to up Prophet's.
So I don't see need to continue going over these previous disputes. It's better to educate Muslims on reality that first generation and second generation of Muslims are still humans. The Prophets are humans too but they are better than the rest. And we have some exceptions like the first four Caliph's, some of the Prophet's descendants like Hassan, Hussein, and some of the exceptional Sahaba. When we are talking really exceptional Muslims(like how Shia think everyone is infallible), they are a very small number and very rare. When the Prophet(SAW), told us of righteous figures to show up in the community from his time to the end times, the only new one we know about is the Mahdi. Which from the Prophet time to now, is 1400 plus years and billions of people. And there is only one very exceptional person between them. And not every single person from Ahl Albayt like Shia seem to suggest.
And that person, like the Prophet's, are given free will. Means they made their choices in life and there was no advantage they were born with, like Shia suggest. Allah(SWT) knows the future and knew the people who will have made the better choices, it doesn't mean he didn't give humans fair shot and free will.
So I think we have done plenty of discussing these past affairs. And we learned Islam from the Prophet(SAW), and almost everything he emphasized was worship and obedience of Allah(SWT) and recognizing our creator. Since he created us to worship him and we will return to Allah(SWT) who is the 'real deal' if you will and he's behind the whole creation and whole Islam, and whole guidance of son of Adam, and fate of Son of Adam in afterlife. So look to him and recognize him is better than disputing little details in past events. Just because we don't see our Lord right now doesn't mean we should forget about him. He was there before us and will be there after us and we will meet him after death God willing on good terms.