So, the interstellar gas also passes through a shock wave as it is diverted to flow around the heliosphere. The region between the termination shock and the heliopause. The region between the heliopause and the bow shock. The inner heliosheath downstream from the direction the heliosphere is moving through the interstellar medium. In fact, a larger portion is neutral matter in the form of atoms, molecules, and dust.
Neutral matter can pass right through the bow shock, heliopause, and termination shock.
However, the atoms are mostly eventually ionized by charge exchange with solar wind ions and my photoionization from solar radiation. Interstellar dust is, of course, eventually melted, sublimated, or evaporated by solar radiation as it falls into the Sun. Very little is really known about the local interstellar medium. One of the many unknowns is the strength of the magnetic field in the interstellar medium. If the field is very weak, then it will have little or no effect on the flow properties.