TBH if you couldn't be friends with someone because they have obvious low self-esteem/self worth and worry about their child getting invested in a friendship then being hurt when it suddenly evaporates, that says a lot more about you than the OP.
OP I grew up on a council estate and went to a very middle class school out of the area. Some kids with lots of money were lovely and I even got invited to a sleepover at a quite fancy 4 bedroom detached house in one of the extremely posh villages near the school. I remember going home and telling my mum about how this house's main living room was bigger than our entire house, and how they had three living rooms!
Some kids with lots of money were horrible and mercilessly teased me. I'll never forget this total arsehole pointing at my Kwik Save No Frills crisps at lunch and shouting, "You eat shit crisps!" at the top of their voice when I was 12. Peak twat, really.
With the decent kids, I actually had no idea how much money they had until I went round their houses or they left for private school. In the case of your son, if the friendship has developed naturally to this point, then they like each other for who they are, and I don't think it will fizzle for financial reasons if you're all decent people.
We live in a very naice town these days. I sometimes get the slight unease of feeling "I don't belong here" when I take DS to playdates (there was one on a private road in a bloody mansion last month and their parents drive a fecking Bentley, and I never even saw a Bentley in my life until we moved here last year), but I tell myself to stop being silly and that the kids don't even know what this stuff costs. Then I go home and tell DH all about the fancy houses DS's friends have and we talk Rightmove or career planning for a bit and think about how we can get ahead a little more for ourselves.
Just give the kids the time and space to get to know each other, and if you're worried, maybe make the first move and invite the other boy to your house early so you can see for yourself that they're totally fine in your surroundings.
It's just another form of imposter syndrome.