The center of our galaxy is way to far away for almost anything happening there to have any effect on us
True in any practical sense, but if a Gamma Ray Burster were to go off in the center of our galaxy with its beam aimed at us it would likely sterilize the Earth except for subterranian microbes. GRBs are rare but GRBs can ruin your day.
Me, I'm much more worried about a car accident, cancer and some fanatical Islamist out to murder my family than a NEO or GRB.