Gravity is not just attraction to the closest thing but also the heaviest thing.

As the galaxies “pass” each other, all stars will be attracted to the dense cores of each galaxy. That is going to change the trajectory of individual stars and, as an aggravate effect, the overall shape and distribution. Unless the galaxies are aligned on the same angle, this is going to drag stars off the primary plane.

As the galaxies approach, the arms will stretch out to each other. As they pass through each other, the planes will tug on each other, and after they “exit”, the arms will reach back.

All this new motion will disrupt the natural shape and trajectory of the galaxy as a whole. Depending on the momentum, it could get pulled back and the whole process could happen again ( and again ) with greater disorder each time.