According to this, North Africa and much of the middle east are 90% to 100% Muslim so it's fair to say that the those areas will be largely depopulated. If 90% of the Christians, Jews & Muslims disappear, we expect 81% to 90% of the total population of these areas to be taken.
Similar situation for South America, parts of Europe (Portugal, Italy, Greece, Poland, etc) and Mexico and central Africa.
US, Canada, Russia & Western Europe are somewhat more secular at 60-70% for US/Canada/Russia and Germany/France around 40% - 50% etc. So we can expect 54% to 63% decline in population in US/Canada/Russia and 36% to 54% in Germany/France.
The only major countries that will not be significantly affected are India and China. They have total population of about 2.5 billion.
So what happens? That largely depends on how the disappearance of all those people is explained. It's possible that Abrahamic religions experience a renaissance with a large uptake in China/India. Depending on how long the situation lasts (If I'm not mistaken fire and brine are to follow shortly?) you can see monastic life return and theocratic rule being established all over the world.
If on the other hand this event is chalked up as a unexplained phenomenon, the world will remain much the the same. In geopolitics, you can expect India to expand into Pakistan while China swallows up Korea and much of SE Asia (vietnam, thailand etc).
The Russians will probably push into Central Asia and Eastern Europe but NATO should be strong enough to stay off any incursions into central and western europe as well as the scandinavia. Russia will take over Ukraine and Germany over Poland to prevent Russian for taking it over as well.
In NA I expect to see US and Canada collaborating closely with the US taking over strategic points in the caribbean (Cuba, Panama).
I'm answering the question as asked - assuming 90% of all christians/jews/muslims disappear no matter the denomination, their devotion or believe in the rapture.