Why can space telescopes see through a planetary nebula?
Let's say we have a spherical shell of some material emitting light, much bigger than the star it surrounds. If we look right down the center of the shell, our line of sight takes us through only a small amount of gas - not enough for there to be significant emission. On the other hand, if we look at the nebula near the outer edge, our line of sight takes us through substantially more material:


Inspired in part by an image in this piece by Phil Plait.
If you look through more light-emitting material, you'll see stronger emission than if you look through less material, so in this toy model, we would perceive the edges to have strong emission. So a spherical nebula wouldn't lead to uniform emission throughout our cross-sectional view of it.
This simple spherical model holds for some cases, but certainly not all, particularly because many nebulae aren't spherical (Wikipedia makes the claim that only ~20% are truly spherical, which I haven't been able to verify.) For example, we know that the Ring Nebula isn't actually a sphere because the central surface brightness is much lower than the projection effect I described above would predict. Something else clearly must be going on. In this case, the discrepancy is solved by the fact that the Ring Nebula is a bipolar nebula, with its axis along our line of sight, with a dense ring of gas around its equator. Therefore, there's more material near its edges than its center from our perspective, and so we see more emission.