Disclaimer: I've never been to eastern europe, and my opinion that I'm about to give is just based on my understanding of European attitudes and identity. I am American
I think that unless you have heritage from those countries and you speak the local language near fluency, it would be hard to be considered a local. I would imagine that the more traditional and conservative the country is, the more this would be the case. During good times, they wouldn't mind an expat christian being around and learning about their country. But keep in mind with the way things are going with the migrant crisis, it will become harder to become a citizen (even legally immigrating and assimilating). You may get some more leeway if you are a practicing member of the local church, but people will still consider you a foreigner. This could have implications on your social and dating life, as a traditional church girl's parents would probably have a harder time approving a relationship with a foreign man than a local man.
I'm not saying staying in America would be a better decision, but it's something to keep in mind.
What is your ancestral background? You don't have to say here or be specific, but if you know when/where your ancestors came from, it would be worth checking if those countries have citizenship/residency by ancestry programs. I'm eligible for citizenship in two Mediterranean countries. I speak one of those countries languages near fluently, and the other is similar enough and I'm learning it easily. One of the countries I have friends and family in, so when I do make the move (hopefully next summer) I have local connections and I'm familiar with the culture below the surface level. I think a set up like this would be ideal in the case of expatriating to europe.
I would also recommend looking into southern south america. Chile, argentina, southern brazil and Uruguay may be what you are looking for. Easy residency/citizenship, developed, good dating life, mostly white, but with easier assimilation than europe. Uruguay and argentina aren't particularly religious countries, but you can find religious people if you try. Brazil isn't as white as europe, but I like where the country is headed under Bolsonaro