I don't think the problem is people's outdated knowledge or belief. I think the problem is people have trouble viewing field as a physical thing. I remember when I was a freshman in college a kazillion years ago I asked my professor what a field was hoping he'd give me an answer in everyday terms I could relate to. He ended up telling me a field is a field and I should wait a few years before it comes to me.
I understand now that asking such a question is like a person who has never seen the color yellow asking what the color looks like and hoping for an answer in terms of his everyday experience. We could describe its effects and how it works. But when it comes to it, we have to understand it in its own terms.
Going back to field, when people refer to physical things, they are thinking of everyday experience physical things. As a physicist, I'm sure you've come across plenty of people who have asked you what an atom looks like. To them, they want to view the atom in terms of what they could understand from their everyday experience. That's what people are used to and that is exactly why
real science is not so popular among the general population.
PS I'd be surprised if you haven't pulled out your hair trying to explain something like the universal expansion of the universe to a lay person before. They live in what they perceive to be a 3 dimensional universe. How dare us trying to challenge this perception?