Actually "Bless you!" (often uttered as "bleshoo") can be considered as the secular (or neutral) version of "God bless you!". It is just so common that it doesn't necessarily have any religious connotations when said and it used used by many non-religious people as well.
Usage notes from Wiktionary:
Saying bless you after a sneeze is not considered particularly religious. Those who say or receive the remark may or may not belong to a religion themselves, and no offense is usually intended by the speaker or taken by the recipient if the recipient is not religious by nature. English speakers not comfortable saying bless you might instead use the German loanword gesundheit.
What are alternative responses for when someone sneezes?
There is this list with some humorous options also. Some notable ones:
- “You are so good looking.” (From Seinfeld episode #38, “The Good Samaritan”.)
- “Salud!” (Spanish. After a sneeze, “Your health.” As a toast, “Cheers”.)
- “Are you okay?”
- Dog bless you!