Dark matter would be hard to compress externally by some kind of wall, but there aren't walls like that in any astrophysical context (other than perhaps magnetic fields, but those aren't active in, say, spiral density waves either). Collisionless does not mean low pressure, so can have high pressure and exhibit the same resistance to compression as any high pressure gas. Indeed, spiral density waves don't separate the stars from the gas, even though the former is collisionless and the latter is collisional. So something a little different than a gravitationally induced density wave must going on in the Bullet Cluster.
Gas pressure is the momentum flux density of the particles, so only requires velocities that are high and isotropic. In short, the ideal gas law. It's true that collisions are useful for maintaining the isotropic velocities (that's really all collisions do in regard to gas pressure), but there must be some other way that dark matter does it because dark matter is normally assumed to be at a temperature. I think it must be its history of obeying the cosmological principle which must ultimately be the source of the isotropy of its velocities. Honestly I am not sure why dark matter is always assumed to be thermalized, and even often treated as isothermal. Clearly the dark matter particles interacting in the Bullet Cluster has velocities that "remember" which cluster they came from, so are not thermalized, yet the Milky Way dark matter is generally assumed to be thermalized. It must have to do with the history.
The confusion about pressure and compressibility in collisionless gases probably traces to the fact that introductory sources often confuse pressure with forces on boundaries next to the gas, which requires collisions with the boundary (though still not between the particles themselves). But the force from/on a wall is actually nothing more than the action/reaction involved in the mundane "normal force" seen in so many other contexts, so is not pressure any more than standing on a bathroom scale is gravity, but it is a good way to measure pressure of gas that isn't dark matter. I don't know why so many sources like to think of gas pressure as a force on/from a wall, as it is more usefully and more flexibly thought of as a force on the gas itself, stemming from the gas itself, stemming from the momentum flux density within the gas. And even though the fluid approximation is made much easier to assume by collisions, it is used for dark matter also. But yes, the Bullet Cluster dark matter is more easily understood not in a fluid picture!