Saying we don't have a class problem in the US is a weird thing to hear.
Social class is everything in the US. We don't talk about it in public, or often in private, really, but it's everything in our daily interactions.

Wealth = status
The appearance of wealth alone gets you a lot of doors opened.
The appearance of poverty will get a lot of doors closed.
We don't talk about it, but it's everywhere. You simply can't miss it.