Out of this huge region, I've only been to the Baltics, but I visited several major churches in some of the capitals that had been destroyed in the war and were rebuilt under the Soviets.
Given that Stalin (and the people he put in power in eastern Europe) opposed religion, why and how were these churches rebuilt?
Resources would have been needed to rebuild the economy and housing stock, and there was no major tourist industry. While they could have been left to rot for ideological reasons, they were rebuilt anyway. Did the Soviets rebuild them to have a bit more prestige, or was this the work of local councils quietly restoring an important part of their local identities?
I can say only for Soviet Union, but they were rebuild exactly because of ideological reasons.
Nazi plans (The Generalplan Ost) for conquered territories of Soviet Union included complete Germanization. Soviet people were meant to be either destroyed or slavered, and their culture destroyed too. The damage that was inflicted upon Russian cultural objects wasn't just a reality of war, it was intentional destruction. After the war, the rebuilding of significant cultural objects, including churches, was viewed as "healing from wounds of war".
Note that many of small or culturally much less significant or known churches remained in ruins until the fall of the Soviet Union. They've never been included in any lists of cultural heritage and because of that they haven't been rebuild.