What would be the outcome for life in our galaxy if the merger of the Milky Way and Andromeda creates a Quasar?
Quasars have very pointed jets perpendicular to the rotational axis of the accretion disc around the central black hole. As long as this jet doesn't happen to point into the galactic plane, the cosmic radiation of these jets won't be a too serious problem.

But a collision of two galaxies can become an eventual problem in a different way. A merger of galaxies triggers star formation and sweeps most of the galaxy free of interstellar dust and gas. So, after a short (hundreds of millions of years) period of time, we'll get lots of new stars. But they'll eventually exceed their main sequence lifetime. Due to lack of interstellar matter only very few new stars will form afterwards. That's a difficult settings for formation of planets and life.