I agree. It is offensive.

This doesn't have any real value in response to your post but your post reminded me of this.

I keep the reply short and simple and as inane and inconsequential as the so called "greeting" or "wish" and it works for me: "thanks, but I prefer not to!

That have a blessed day thing has become the Christian secret handshake, gee I'm sorry you live in a judeo-christian world.
it will do you no good to try to set your self apart.
it is best to keep in mind the water in which you swim it may be tainted but it's the only water we have. and feel free to vent your frustration with me.

I have come to the conclusion that no one really truly believes in God. They think they do but when the chips are down most will revert to an animal state. Kill or be killed, survival of the fittest, etc. I am fortunate that I work for an extremely progressive company where he would be set straight or let go if he kept up this chatter.

'Blessed be' is how pagans greet each other. Generally meaning, 'enjoy the fruits of your labour and the joy the world has available'.
[learnreligions.com]

I think some people use 'blessed day' the way other people use 'Oh God', it doesn't really mean anything other than have a good day.
Personally I find being honest about my atheist views but not pushing them has been good.
I hear 'Everything Happens for a Reason' A LOT! And crazy part is it's from my pot smoking, heavy drinker, nudist Christian friends... I usually reply gently, that I don't like that phrase that I prefer to think, "With the right attitude most situations can be an opportunity to learn and grow into something better."
Most of the time the response is WOW, I like that a lot better.
If they push I'll say, I don't like the idea of someone or some entity intentionally bringing pain.
This past weekend someone I talked to that way, gently, not from a place of offence, actually came to me and shared that she is having doubts about her faith.
We need people who give the 'hail satan' response, but I think a gentle response goes a long way as well.

Yeah....good luck with that......or, you could spit in their face.after thinking it over...that might be too much like an assault

First, my sympathies for working retail, a thankless task. As for the Have a blessed day, watch out for the crap list jobs that you can be assigned. Worked for a christo-fascist at a big box store, unless you were a fellow believer you got the crap times to work including the open on Sunday and open on Monday!

Ask him if he's seen The Handmaid's Tale.

I usually respond with "have a good day yourself" if their aware enough, they'll figure it out.

It seems the use of "blessed", "blessings", etc., has come into vogue as a warm greeting, and not necessarily that of a religious nature. It is viewed as particularly non-specific to any line of thought and, thus, hoped to be easily received without offense.
Always best to assume good intent unless, as others have offered, you would not be inconvenienced by losing your job for snapping back with a verbally aggressive retort specific to certain beliefs. Oh, yes, that would be accepted by H.R..

I just say back. "And good luck to you"

You should reply with have a blessed day too!
Blessed by whom is where the can of proverbial worms come into play!

It's very annoying. I'm doing Uber to pay for classes and I often have to nod my head and say thank you when people say that to me. I hate the assumption it makes and yet I'm forced to tolerate it if I want good ratings. Of course I think you should be free to reply hail satan or whatever you feel like but I know that's not the world at live in, there are consequences. I hope we live to see the world change and humans outgrow such primitive and repugnant ideas but it's hard to imagine most of the indoctrinated ever waking up and letting go. Sad and frustrating.

Maybe "Have a gesundheit day"? Seriously, if it sets you off, that's too bad. How much do you need this job? I'd blow it off if I were you, but it's up to you.