Is our moral obligation to not do harm, as opposed to preventing harm form occurring to someone else? Am I in the wrong for not donating money?
Insulating people from the immediate harm consequent on their foolish or evil conduct is notorious for encouraging people to continue to act in the same way until the consequences can't be stopped and the harm done -- to the person acting, or innocent bystanders -- is much greater than it would be to allow the first harm to happen.
Hence allowing harm to happen may in fact be morally required.
Is it always wrong to allow harm to come to someone?
No. It is because it depends on the situation you are bound in. I mean Dharma. But we should not allow harm to come to any person often if it is right to protect him.
Just think of this situation -- Is it your responsibility to save a person who has been sentenced to death for a terrible crime? 'No', isn't it? So we can't say, 'Yes' to your answer.
You would get so many instances for this from the history. You could read it in the Mahabharata also -- about the 'indifference' of the audience (Adharma) due to the binding with the Kauravas at the time of 'Cheer Haran of Draupadi'. From this you would understand that not only allowing but sometimes even indifference would become wrong.
Am I in the wrong for not donating money?
Sometimes. You shouldn't forget that the money you use is not a thing that is not earned completely by your own effort. Most people wouldn't agree on this idea. But if you could think better, you would agree with me. So you should donate money according to the situation and considering your ability. Sometimes the money may reach some immoral activities . So you should also consider where the money goes.
Just for a thought: https://www.holy-bhagavad-gita.org/chapter/3/verse/10
But don't forget that the above link is not about donation in the form of money. It is just for reminding people of the truth about the interrelation.
So, helping / serving is the more important thing.
We must act toward others with their best interests at heart.
Now with respect to circumstances, we have found ourselves in. I don't know who you are and what is your purpose here and in life. I can only tell you how it looks from my side of the table.
I see a p-Zombie Apocalypse. I see generation after generation of human children being put through a standard series of severe traumas -- so bad, they are forced to give up trying to develop their humanity, their conscious, rational Self. They do it to escape from fear and pain, and they might get some reprieve. But they will be paying price, they will continue to suffer from the so-called "human condition" -- a combination of existential dread, chronic anxiety, depression, PTSD, impostor syndrome, personality disorders, etc. -- for the rest of their lives. And that even before all the blows they are trading with others, and the next generations, to keep the vicious cycle of violence going, to power the machinery that churns human children into mindless drones.
I don't know who is behind it. I don't know if they themselves realize what they are doing. I know that many prominent people voicing similar concerns had died, or disappeared (according to my Internet). But, honestly, I don't know what makes you think that I can simply drop the subject.