Can you ignore a child who is screaming because they aren't getting their way?

I can. I can completely tune it out and ignore it. In the beginning (40 years ago) I found that very hard to do and I’d feel my temper rising right along with the screams. We’d end up in a screaming match, which was stupid and counterproductive.
But over time I got the hang of it. Doesn’t faze me a bit, so scream on, kid. I don’t mind, and it’s not going to change a thing.