1) The Apollo mission controllers DID pay attention to Solar activity, which affects the thickness and intensity of the belts as well as the radiation environment farther out. A big solar flare might have delayed an Apollo launch, waiting for things to settle down. Even with that possibility, though, passage through the fringes of the outer belt would not have subjected the astronauts to a really serious radiation dose.
2) The inner belt is higher than Low Earth Orbit, where most of today's satellites go. A solar flare might delay the launch of a GEO satellite, but I've never heard of it happening.
OK, one last thought: Van Allen belts sound a bit like Earth has a volumnuous but not so massive, ionized hydrogen outer atmosphere layer.