You can try to guess who I’m talking about

In fact, both of them adjusted their glasses in a way that “hides” their eyes.

It's kinda logical, if you're made fun of for smth, you'd wanna hide it

I know one of them is Milhouse.

What makes it funny is how they were both called “four-eyes” by an arrogant, blond-haired character

I mean, that's how you make fun of people with glasses. If you know a few characters with unnatural hair colours, it's likely you'll find two wearing glasses and being made fun of. I guess they're quite common in anime which you mentioned you watch, but I don't.