I think I understand the intent of your post.

I travel frequently with work and I think you’ll find most western countries to be more accepting of atheists than the US. The US is the only place I’ve visited where church seems to get mentioned pretty frequently. Which is maybe why you think it will come up in conversation?

Enjoy your travels!

First off.... don't tell people in another country your an atheist. Who really gives a crap until you tell them.

I am not sure how serious you are on such question...... I am sure everybody agrees that it's common sense that you should follow common courtesy (and the law of course, that goes without saying) wherever you go. Specific examples... Thailand, when you go through immigration in Bangkok, there are signs at passport control where specifically said things like "getting a Buddha tattoo is a no-no" (It wasn't worded like that but you get the gist), also other signs with warnings like "Making fun of Buddha is not cool" (again, wasn't worded like this but that was the idea)...Plain and simple, you can't go around yelling stuff against Buddha because it will get you in trouble (common sense). Singapore, before landing you will receive a small booklet with all the things punishable by law, things like porn (and then you freak out wondering if they are going to scan your laptop...so make sure you bring your business computer where you don't do any dirty laundry just in case... they didn't even ask and yet, you feel threatened), another one.. freaking bubble gum.. don't you dare throw it on the street, they will do horrible things to you..that's what the booklet says and I was NOT going to test their will.. I know better..... that should suffice to establish a criteria... if you are in another country then you should treat them with respect if you are expecting the same in return. That's my two cents....

Better pretend to be a theist, nod and believe everything you're told. You'll blend in nicely

You know how you don't put an 8' x 4' sign on your front lawn that proudly proclaims:
'I'M AN ATHEIST'. Well for most of the world it's like that too. I have travelled and lived extensively in South America, the Caribbean and Central America, these are areas that have a strong Christian following, mainly Catholic. While many of these Catholic are lapsed and jaded they still don't take kindly to people being Atheist, even Brujas are more accepted, but if you just keep it low key then you should have no problems.
There are parts of Africa you should really stay away from, those countries that lump Atheism in with Homosexuality and make it punishable by hard labour, imprisonment or death.
Here's a link. [theatlantic.com]

Just don't tell anyone.

I would suggest not to be too open about it is certain parts of the USA.

I'd avoid Saudi Arabia etc