Even if it has nothing to do with the Rapture, you don’t need to be an adult to “profess” being a Christian. Toddlers can tell you that they’re sons and daughters of God, and they can sing you songs about Jesus loving them etc. That’s probably good enough to count as Christian to any mechanism doing the sorting, especially if adults who merely publicly claim to be Christian will be taken.
As for what happens after this event, I also assume most people left behind will attribute the event to the Rapture, regardless of whether it was or not. But I’m not sure that conclusion will turn many people Christian. Isn’t there supposed to be 1000 years of the devil ruling the earth after the Rapture? If people believe that it was the Rapture, and find out that Jesus won’t be coming back for a thousand years - there will be plenty of bibles laying around to consult after all - it doesn’t sound like a huge incentive to try to believe given no one’s going to live a thousand years. I know that 144,000 Jews are be saved after the Rapture to be God’s army, but there isn’t a lot said about the fate of everyone else left behind that I’m aware of.
Not sure if the OP wants to look at the religious ramifications, or just the societal / logistics / power aspects.
As a non-christian, who has pretty firmly declared my non Christianity on multiple occasions, I’m not sure that the link to Christianity under the stated circumstances would be immediately apparent.
For many of the people I work with, I wouldn’t know whether they were Christian or not, and I would think (at a guess) that the are a whole bunch of others that consider themselves Christian, but still outwardly practice other faiths for the sake of appearances or expediancy - will they disappear? If so, I would think its going to muddy the waters somewhat.
Immediate thought would be to have China take over North America. Beyond that - there would be no idea.
Because many other nations like France, Germany have good relations with Israel I don’t think so. I would not be surprised that France, Germany and others will be offered a lot of the resources of America in exchange for cooperation.
Too far, China still has not a very sizable Navy and American Nuclear weapons would still be a big disincentive to invasion.
Come to think of it, the USA would have less to worry about civilian casualties so I could foresee the use of them in American soil if an enemy army is coming to shore.
I think also that as most of the reminder of the Americans will not be as anti-immigrant as the ones that left, I foresee millions of European immigrants coming to America before any military invasions are considered from other nations. It would be an amazing sight to see all those massive new citizen swearing ceremonies.
There’s a theory, taken about as seriously as the rapture by most scientists, that the universe is just a computer program running in a super universe. Seems to me that the specifics of the op - with any profession of Christianity being enough to see you gone - would point towards a glitch in this software system. If this idea took hold, it could lead to an abandonment of all religion, and be seen as evidence of that theory.
Utter chaos would break out on the planet because if all the Christians disappeared then that means that the Spirit that is restraining all evil on this planet has also departed.
Most of the simulation hypotheses I’ve heard of talk about simulation of the fundaments of a universe,. with everything else happening as emergent phenomena (just like they do if it’s not a simulation).
That being the case, the dissapearance of a single category of emergent phenomena would be hard to explain. A glitch in the simulation should change something fundamental - affecting a lot of different things in the same (or related) way, or possibly annihilating everything.
But not impossible. After all, the universe program presumably has a use. Perhaps a PHD student is studying religion on this planet, and stores all the christians in one place, that gets wiped.
It’s not terribly likely, but the event posited in the OP is an unlikely event. There will be people who assume a religious explanation, but equally there will be people searching for a physical explanation.
One third of the world’s population gone, and China and India are still overcrowded.
I suppose what would happen depends on how much the remains of the UN want to sort out the remains of the world. China - which would be far the most powerful player in world scene - aren’t that friendly with the West, and have a traditionally insular culture.
Having thought about it a bit more, I think local governance in the US may well continue - the US is a lot better at that than the UK is. I suspect the federal government may well cease to exist, though. I wonder if the power stations and water supply systems would continue if half the country vanished?
But even if the aliens did it, billions remaining would still assume that GOD (in one form or another) led them to destroy Christians. Hell, the Islamic world would probably assume that from the beginning, so there’s 1 billion people assuming GOD there.
After all, the defining characteristic of the people missing was their religion, so obviously religious implications and scenarios would arise regardless of the means of disappearance.
There would immediately be conspiracy theories claiming that Christians had all gone into hiding in underground bunkers and were about to unleash some kind of death above ground to take out their competitors.