I hope you don't mind me saying this, but it appears you're comparing apples v. oranges here.
The incident with the cashier, definitely seems like a classic microaggression, at least as such as been described to me.
But the school issues with your sons go way, way deeper, I think, than microaggressions. They're indicative of a profound vein of systemic racism likely to impact Black people & people of color throughout the US.
My own experience is that I was on the PTA at Brooklyn's PS 8. Our president & I became friends. He was deeply involved in his son's education, but after several years in a public school that pre-dated the Civil War & was set in Brooklyn's oldest & wealthiest neighborhood, Robert concluded that the system wasn't equipped to educate Black youth—boys in particular—& pulled his son from the system in favor of a private school (Friends Academy, I think).
Bear in mind that Robert had been deeply involved from the get-go, & still couldn't make it work to his satisfaction. While he never openly cited racism as the cause (at least not to me), what else could it have been?