Why can I see the Andromeda Galaxy despite Milky Way's rotation?
As barrycarter already pointed out, it is due to the huge time it takes for the milky way to rotate.

For once, as he pointed out, the stars in an orbit similar like the sun take about 250 million years for one full revolution around the center of the galaxy. If you put that in a relation to an earth year and take our civilization of roughy 6000 years of keeping records in comparison, we exist roughy 12 minutes of our galactic year. If you only take the last 150 years of the modern era, it's down to 18 seconds.

So if you compare that, how much does Earth move around the sun in 18 seconds? That is about how much Andromeda has apparently moved relative to the constellations in the night sky since we can capture visual images on film.