This NW Kansas town has a population of 2800-3000, one grocery store, one "department" store, a Dollar store (maybe that is another department store) and 4 gas stations. There is a prison but their numbers are not included in the population count. There are 8 eating places in town and 8 churches. Works out since lots of the attendees of the 8 churches go to the eating establishments for Sunday lunch.

No religious flyers at stores but one church routinely mails out invites to events like Easter services, "friends and neighbors" Sunday or Christmas. Religious greetings in public are not common but a sneeze merits a "bless you" in many instances and any tragic, distressing or stressful event will prompt a flood of "thoughts and prayers". Overall pressure isn't high and I know there are a lot of people who don't attend church or only attend occasionally but you have the sense that public proclamations of non-belief could make you a pariah.

We have 2 churches, 5 liquor outlets. I guess that sums us up.

I would have to hand those flyers back, or better yet just request they don't put any in my bags to begin with.

I grew up in a town with a population barely north of 200. It has two churches, a tavern, and a tiny store that added a gas pump around 1999 or 2000. The members of the Assembly of God Church very much cared whether you went there and would try to recruit. There was a lot of "you know, you should come to our church sometime. I really think you'd like it there." The Presbyterians were fine.
I went to the AoG when I was a kid, and my parents didn't. They dealt with a lot of judgment, and I definitely knew that I was in a different situation than other kids.
Yours sounds a lot less hostile. Fliers and blessings would be fine.

My town is even smaller, but I haven't run into it as much as you describe.

Medford, Wisconsin here, bro. I feel ya

Wow I have approx 25,000 in my town-no prisons, less than 10 churches I know of, 2 large Shaws Supermarkets within 5 miles of each other, multiple registers. Easy to avoid any religious zealots by changing registers.

Sounds like where I grew up. They'd also decorate the side of a specific stretch of the highway with these super-religious signs that had way too much text on them. Bloody road hazard.

small town but not religious in that way

I live in an area loaded with churches, too. "Have a blessed day" always throws me, though. I feel awkward returning the sentiment, but almost as awkward in saying something else like "have a good day", when they set the tone. Still trying to figure that one out. ?