Colonial legacies include language, religion, food, mannerisms and other deep cultural ties. Independence doesn't mean unrelated. The word 'independent' would be unnecessary if there was nothing in common. Kyrgyzstan is geographically isolated, but is right at the heart of the Silk Road from which ideas and armies have flowed from China, India, Persia to the Mediterranean. Kyrgyz is one of at least 35 Turkic languages. The country also had more than a century of Russification as Russia implemented cultural assimilation. Extensive contact, evidenced by language traits, existed between Proto-Turks and Proto-Mongols. 'Kyrgyz' derives from a Turkic "we are forty" which came from a legendary character who united forty regional 'independent' clans. They had been fighting, but to fight - you have to care about something in common. As Nomadic people, the Kyrgyz tend to move back and forth over the mountains depending on where life is perceived as better. Better rain or better government.
Eastern Orthodox Christianity
Asia including Turco-Mongol Nations - 1335
Golden Horde and Chagatai Khanate