First I have to say I like the custom because it is a automatic response that in many instances is said without thought or intention and totally socially acceptable anywhere.
It allows you to bless someone intentionally without explicitly do so or even asking permission. I’ve had instances where I would like to have God bless someone, and then they sneeze which allows me to do so.
It also allows you to accept a blessing through others. In the realm of faith, the intention of the person in giving and receiving is important for that person, so even if the person is saying it unintentionally, you can still receive from God intentionally.
I usually go with “Gesundheit” or “salud”, but will occasionally say “bless you” to add variety.
Yeah, some people say the “God” part, and a smaller subset of them emphasize the “God” part. Instead of “gublessyou”, they say “GOD blessyou” as if invoking deity is going to make me sneeze less. I’m not bothered by “gublessyou”, but I am a little peeved by “GOD blessyou”-- it’s like they’re trying to prove that they’re more pious than anybody else by emphasizing their invocation when responding to my sneezes.
I’m a kinda-sorta believer of a non-Abrahamic variety, so I try to keep my sneeze reactions pretty neutral. I’d feel really silly saying “Eir bless” every time someone sneezed.