"Coming out" as atheist or agnostic

Rawr • Swedish. Love red pandas ❤️️
Hi there! First of all, I hope you all have a great weekend!
I just got to thinking the other day about how all of you have approached telling new people/extended family about your beliefs (or rather lack thereof!).
Even though I've moved around a lot my whole life, it never was an issue for me until recently, which I find really curious. I was either surrounded by people similar to myself or with people who were sensible enough to realize that my lack of belief didn't affect their beliefs. 
However, lately I've noticed a number of people who seem to take offense at the fact that I don't believe in God; nor care to. It's rather frustrating and strange for me since I've not had to deal with it quite literally in my face before. 
I've tried to be as diplomatic as possible (I like to abide by the "rules for polite company: no talk of sex, politics or religion" unless it's people I'm comfortable with... And also because if I don't know someone well, I don't really care what their thoughts on the matter are.) but it gets really difficult when I feel people get either aggressive (scary!) or high and mighty (I'm ashamed to admit it but it makes me want to put them in their place) when confronted with my *gasp* heinous non-believing ways... Which are actually pretty much the standard in Sweden, where I'm from. (While the country is technically Lutheran Protestant, only about 18% of people openly state to believe in God, and only 4% attend church with any regularity. A lot kids (esp in the countryside) only go to church at the beginning and end of school year... And that's to use it as an auditorium because they don't have one, or at least not one big enough!)
This ended up WAY longer than planned, but I'm really curious about how all of you deal with this kind of situation.