I don't separate the two at all. Many of the songs are political, too, in some way shape or form, even if it's not obvious.
Mostly I support the things Morrissey has stood for in the past. Mostly his opinions align with my own. But on the subject of animals, I've always dismissed him. When I was 14 I listened to "Meat Is Murder" and, believe me, I desperately wanted to agree with the logic in the song. I really did. I wanted to make that song into a banner under which I could march on a crusade. It took all of five minutes for my adolescent mind to puzzle out the logic, though, and it didn't hold water. Meat is not murder. The slaughter of animals for meat might be cruel, unnecessary, morally repugnant, barbaric, catastrophic for the environment, and produce unhealthy food for humans to consume. It isn't murder; "a death for no reason" is laughably inadequate as a definition of murder. It's obvious what he means, but it falls apart under scrutiny. So even back in the day I just said, "Okay, he feels this way at a level beneath, or perhaps superior to, logic or rational thought". Which is fine, in the end, but he's never going to convince me with his arguments. Now, showing seal pups with their heads bashed in, thrown into the middle of a video ("Interesting Drug"), that might do some good.