I’d never say “God bless” to someone but “Godspeed” seems like such a cool if somewhat affected farewell. Does it have a secualar usage?
It translates from Middle English as “May God Prosper You” so I would tend to say not. OTOH, saying “God Bless You” is hardly a public declaration of faith so you be the judge.
And “good-bye” comes from the phrase “God be with you.” Can an atheist not say “good-bye” unironically?
I’m an atheist and i have no problem using religious language. Since most of the religious language is used socially and not literally, I consider it my cultural inheritence as much as anyone’s. It’s not like you’re actually thought to be summoning God when you say “God bless.”
Also my disbelief doesn’t prevent me from wishing something. I may not think it’s going to happen, but it would certainly be nice if God helped somone. It’s not like I don’t wish God would speed somebody along or bless them, or whatever. I’m just skeptical about the probability that that could happen. Also people ask me to pray for this or that every so often and I say I will and I do. Disbelief doesn’t even stop prayer as far as I can see.
My position is similar to uglybeech’s. I don’t have a problem with the casual use of language which has been acquired from religious context…it’s overtly religious use of language that I find difficult to accept, which is not the case here.
On a different tack - can anybody use ‘godspeed’ without irony?
Etymology is not meaning. An athiest may use any phrase he or she wishes without irony so long as the intent of teh message is not the opposite of the apparent message.
Haven’t you heard. We do most anything we want! 
Can a Christian Englishman use the expression “by Jove” unironically, without intending to honor the pagan god Jupiter (aka Jove)?
Can a blind man say “See you later” or “good to see you” unironically?
The answer in both cases is, of course they can and of course they do!
So I would suggest people use whatever standard words or phrases they like, without worrying about the implications. If someone sneezes, feel free to say “God bless you,” even if you don’t believe in God. It’s not harming anyone, and you’ll just give yourself ulcers if you try to purge your speech of all phrases that might have hidden religious meanings.
Sure. I know that in the Lutheran church (ELCA), at least, there’s a ceremony of godspeed that you can insert into the worship service for somebody moving to a different country (or wherever).
I’m an atheist who doesn’t say “God bless” but says “God damn it” very very often.
Without attempting to be too harsh, would the OP argue that an atheist could never take a holiday (holy day)?
The OP’s not just athey, he’s the athiest!
sorry
While I say “bless you” in response to a sneeze I would never say “God bless you” in response to a good turn. (although I would say “God damn you” in response to a bad turn) I’m not sure I could say “godspeed” without it sounding mocking or insincere.
Personally, I would restrict my use of “godspeed” to situations where it could be used appropriately. For instance, “Godspeed young Master William!”, followed by the sound of hoofbeats fading into the night.