I think you will always have a hard time convincing poor white people of the idea of privilege. Things aren't great in trailer parks. Race and class do go hand in hand in terms of people's experiences.
Agree with hanimal that it's the word privilege and what it means to different people, how they understand it, etc. When you break down what types of things you are calling privilege, makes sense as it defines the term, but just saying white privilege/privilege is not going to get the discussion to go anywhere if you aren't already talking to people that are on board with what you have to say.
Something to think about is there are many poor white areas where the education system is pretty damn bad. You are trying to have people understand the world from someone else's perspective without really giving them the tools to do that. It's like wanting people to have a real solid understanding of critical race theory, the high level college topic that it actually is, when they dropped out of middle school.