As Russian forces approach Father Fedak’s Greek Catholic monastery, a wider ecclesiastical flight is happening in Ukraine. When Russia launched its invasion in February, the ground war was coupled with a spiritual one.

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In Moscow, the leader of the Russian Orthodox Church, Patriarch Kirill, blessed Russian troops and proclaimed the war in Ukraine a metaphysical conflict between the faithful of God and a decadent West. That has sent officials from other denominations fleeing to the western reaches of the country to escape the fighting.

The émigrés include Ukraine’s Catholics, Protestants and members of Ukraine’s own Orthodox Church. Even some clergy of the Ukrainian branch of the Orthodox Church long under Moscow’s putative control fled as its leaders in Kyiv denounced the war and declared the church’s independence.

The geographic shift underscores a broader spiritual schism under way since President Vladimir Putin first seized Crimea and covertly invaded Ukraine’s east in 2014. Russia’s Orthodox Church has undergirded Mr. Putin’s geopolitical ambitions, holding Russia to be a defender of Russia’s Christian civilization and therefore justified in seeking control over countries of the former Soviet Union and Russian empire. Patriarch Kirill has called the war a necessary struggle whose outcome will determine “where humanity will end up, on which side of God the Savior.”

Critics of the Russian church call it a spiritual land grab.

“For the Russians, the religious sphere matters, and wherever they take territory they want to understand who is important there,” said Ruslan Khukarchek, founder of a Ukrainian-language Christian newspaper, the Cornerstone. Wherever Russian troops arrive, churches have reported visits from Russia’s security services informing them that they need to register their activities or cease meetings, he said.