I ask because it is controversial because it looks like the nazi eagle and I know slayer are not nazis but would it be ok to wear in public or should I just buy a different shirt?
Just don't wear it in Germany. I've got a Melvins shirt with an eagle logo on it and I got publicly shamed and almost refused entry to a club because of it. Had to turn it inside out in front of about 200 people waiting to get in.
In fact yeah, do what Phylactery said. The album covers are much better looking shirts anyway.