Relative distance does change, but the galaxies aren't being pushed apart, rather more space is appearing between them, like a balloon being inflated, if you put 2 dots on the balloon then blow it up the dots don't move, rather the space between them grows, so they aren't moving faster than the speed of light, it is only faster when observed relative to an observer with enough distance.

When it comes to distances far enough out that they are receding away from an observer faster than light can travel the information from them is lost to the observer, without FTL travel the observer could never reach those locations so no information is traveling faster than the speed of light.