Some time ago I lived with a Mongolian student for a while and I was really surprised to find out that Cyrillic is the default alphabet in the country.
My language is written in Cyrillic and while most Cyrillic languages come from the same Slavic language family, Mongolian has very little similarities with the rest.
The same used to be true of the Romanian Principalities until the middle of the 19th century, when we switched to Latin alphabet in order to underline our Romance-language roots and to culturally distance ourselves from the expanding Tsarist Empire.
Of course, the Soviet Republic of Moldova used the Cyrillic writing for Romanian throughout most of its existence, the people over there switching to Latin alphabet in the dying days of the Soviet Union was a prelude to their independence (I have two books in Romanian and using Latin alphabet published in the Soviet Republic of Moldova towards the end of the ‘80s - 1990, priced in rubles and all, really cool).
My language is written in Cyrillic and while most Cyrillic languages come from the same Slavic language family, Mongolian has very little similarities with the rest.