I too am an atheist and have felt an aversion to the bless you phrase, but that's only part of my issue with the whole sneezing etiquette (because if I'm being honest I still use "oh my God" and other such phrases).

The second part of my aversion is the fact that when I sneeze I have a recovery period after the sneeze and when someone says "God bless you" I feel like I have to let out a quick "thank you" or "excuse me" or something and it feels pretty annoying. Like, hey can we just move on and not have to do this strange back and forth thing?

AAaaannd then there's the people who sneeze once, and then again, and then again and you're stuck saying over and over and over again "bless you" while they try desperately to force out a "thanks" before sneezing again. The whole thing is a mess that serves no purpose and I just ignore people who sneeze now. If they want to think I'm rude, well, that sucks, but at least I don't have to deal with all the issues involved in the whole thing.