Space crap is a lot less dense than you might think. Generally speaking, flying through the asteroid belt edge on looks like... well, just flying through space.

Turn it around: the space crap doesn't really prevent us from getting good views of Jupiter, Saturn, etc. Right? And it wouldn't prevent us from seeing Mars or Venus if they were outside of the belt either.

The total mass of the asteroid belt is estimated at something like 5% of the Moon's, and a third of it is accounted for by Ceres alone. It's spread pretty darn thin.

The Kuiper belt is much more massive, but is spread out even more thinly. Same again for the Oort cloud, where the average spacing between comet-sized bodies is about the same as the distance from Earth to Saturn.

A favorite quote from a relevant reference work: “Space is big. Really big. You just won’t believe how vastly, hugely, mindbogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.”