I am always polite, I respond have a good day thank you

Words and phrases aren't really important, but the thought behind them!
ppl and Animals show their kindness with their own language, it doesn't matter what they say; Hello, Hola, Shalom, سلام or Licking your hands and face... it simply means their regards and kindness, so respond it politely and be happy.
don't forget, we accuse religions of the lack of Tolerance and 2-side understanding!

I do the "you too" answer. One older woman who works at the grocery says this every time but, I start the conversation by saying hi first to her every time when I see her. I really have no problem what others want to think unless they go out of their way to try and "recruit" me and I have never had that happen.

"You too ! "

While I hear what you're saying about the God Cologne, the correct answer to give might be : "What do you mean by blessed? Could you explain the word blessed for me?"

And who wants to get that ball rolling?

There are words and there are intentions, sometimes you just need to sort through the wheat and the chaff

'Reason and logic be in your mind.'
'Live long and prosper.'
'Yes, blessed with the freedom from non-existent gods and myths'.
These are a few I use.

I say, "Thanks, you have a good day too."
Ha! Nailed it.
You're being polite and gracious, while rebuffing their religio-speak at the same time.

I say "thanks, you too". It is only words, no big deal.

Thanks, fucker?

Nah, I will just be polite and tell them to have a nice day.

I just say, thank you, you too.

"Back atchya, have a good day."
No harm no foul.

Fortunately we don't have that problem over here. All you will hear is "have a nice day"

I get something like this many times a day, I work customer service for a large financial organization. I usually answer with "Thanks, stay safe out there." And then I d/c the call because I'm trying to keep my call time down and hoping for a nice breather between calls.

“You, too.”

If someone says “god bless you”, I usually ask which one? And if they say “have a blessed day” I just smile and move on as it’s usually someone at a business who thinks it’s a nice thing to say.

Thank you ... have a great day.

Usually w a smile and a nod +/- a "you too!". I've learned to respod to the kind intent, rather than the literal phrase.

I'm a "You too" sort of guy.

"Under his eye"......and then laugh hysterically.

Mostly I just nod and move on. One time I remember because I am a smart ass, I said, 'what kind of day do you think I'm having?!?! There's 2 bags of potato chips in my cart instead of one!' I laughed and left.
Thing is that phrase never use to grate at me and for the most part it still does not until the times it does feel like your description - god cologne splashed at me.

It depends on what I want/need from them.

If I expect something from them I just acknowledge that I heard it and go on -- sort of 'you too' or something.

If all else is the same to me, I say 'No. I'll pass. Thanks.' Maybe they'll think a little without getting defensive. I'll explain if they ask.

That saying irks me to death. Whether it is said as a "blessed" day or a "bless-sed" day it still gets me. My thoughts are "who are you to tell me what kind of day to have." My upset is because it is used as a religious phrase of course. I don't want anything to do with your religion. If I tell you that I am considered hostile. My answer is usually just a "you too." I don't mean this but I do not want to wish them ill or anything. Now, going back in time on this, I had the same problems when others started wishing me a "good day." Yes, "have a good day." WTF are you to tell me that?

Like Moravian, I am fortunate in that, I have never heard it.

After much practice, I now reply immediately with, "Blessed be the Fruit." That's very effective with believers who have seen at least one episode of Handmaid's Tale. It lets them know that I KNOW about the deep shame of christianity run amuck.

I think people in the UK are unlikely to encounter someone who will wish them to "have a blessed day". If it happened to me I would probably just smile and walk on. Of course, some people might use it as an occasion to vent their frustrations and third degree interrogate the well wisher as to his or her intentions.