They don't collide but they do get "tangled" in each other's gravity. Small things (stars) get tossed in random directions and big things (gas clouds) pass into each other and start condensing into smaller/brighter things.

It can't be in each other's gravity, else the same phenomenon would affect dark matter. For something to affect regular matter but not dark matter, it has to be an electromagnetic interaction (at this scale - as the weak and strong forces only interact on very very small distances). So it has to be a significant amount of head-on collisions, or some kind of charged dust clouds projecting large EM fields.