Much more likely is that the galaxies will zoom relatively close to each other – say, a little under 500,000 light years away.

In To Sleep In A Sea Of Stars by C. Paolini, there is a group that aims to prevent or circumvent the heat death of the universe, although the post-human civilisation has barely touched a few star systems (<30 ly). In a similar fashion, I recommend to take the necessary to build up a galaxy defense force soon.