What type of cat is Garfield, though? Or Heathcliff? What kind of dogs populate the cast of The Dogs of C Kennel? As far as I'm aware, their breeds have never been mentioned. And the impact on their stories? None at all. In fact, I'd be willing to bet that most people never even thought to consider what breed Garfield might be; it's that inconsequential to the story.
So why would you care about what "breed" of humans are in any given story?
I'm not saying race is inconsequential and we should be completely color-blind to it, but it doesn't have to impact every story. Marmaduke's great dane-ness is relevant to the stories Brad (and later Paul) Anderson want to tell. Garfield's specific breed doesn't appear to hold any interest to what Jim Davis is trying to say, so it's non-issue there. Readers have innately understood that and, consequently, don't care.
So why should you care that Hulk is Asian? Or Captain America is Black? No one seemed to give a damn when Psylocke got switched from British to Japanese -- since race wasn't an especially significant part of the stories being told at that time -- so why would it matter now?