BUENOS AIRES — The young couple was determined to leave Russia. Alex Slepenkov, 36, knew he could be forced to join the military and fight in a war he had tried to protest. He and his wife, Natasha Slepenkova, 30, feared the country would turn into North Korea, closing its borders to the world. After they learned in September they were expecting their first child, they began looking up alternatives. The couple settled on a destination about as far from Moscow as possible, with a culture and language vastly different from their own. Argentina, unlike many countries, still allowed Russians...