It looks like its orbit is actually within the orbit of Pluto at one point, and at times, the two bodies could come within a very small distance of each other. Wouldn't this disrupt one or the other, possibly throwing them off of their orbits?

Part of why Pluto was demoted is it's so small it doesn't effectively clear it's own orbit. Orbits can look close here but with how small Pluto is it's gravity would barely affect this dwarf planet. It's also possible they've only been at their closest approach a handful of times in their entire life.