"They ask for respect and equality of others but don't wish to give it to anyone who doesn't agree with their ideology."

In this case, "doesn't agree with their ideology" actually means, "Believes that many classes of people don't deserve human rights".

What's funny about your comment is that it's ambiguous whether you're calling the Trump officials or the protestors yelling at them petulant children.

Why does it have to be either/or? It could be both/and.

But in the instance of the comment in question, I think it was pretty clear that it was the protesters who were acting like petulant children.