I think the two events you are comparing are hardly comparible apart from the fact that you could see both the GDR and Nazi Germany as anti-clerical. But the development during and immediately after WW2 is relevant to what you might seek:
The Catholic and Protestant Church organization had an ambivalent and complex view on Hitler and National Socialism. On the one hand parts of the official Church organizations operated under the premise "the enemy of my enemy is my friend" meaning that their hatred and also fear of Communism meant supporting that part of Hitler's ideology that so strongly opposed Communism. This also led to Church members being forbidden to even join the Social Democrats/Socialists even though there were Christian members among them already. But that might for another answer.
Especially the Protestant Church was not a big fan of the Weimar Republic and democracy at all. They still saw themselves as a state Church representing the natural order meaning a monarchy determined by Gottesgnadentum like before World War I. And they were very quick in giving their blessing for the Invasion of Poland and France since in their view it was the duty of a Christian to be a loyal soldier to your country and being a soldier was in their eyes one of the highest forms a German Christian could achieve. In a way you can read this the same way why the old aristocratic officer and military class supported Hitler, they dreamed of a return to the "good old days". The Catholic Church was not so quick in blessing the soldiers or the operation in general but they did hold services for the fallen for example.
But and that's an important But: Quite a few Church officials from the Catholic and Protestant Church saw National Socialism more skeptical. First of all Hitler had already passed legislation against the Churches and made no secret about the fact that he wanted to "overcome" (eg. get rid) of them. And certain clerics asked: If we are so scared of Communism and their prosecution of Religion, why aren't we scared of the Nazi movement which likely could go down the same road?
Like with many things in relation to the Third Reich you also need to take into account that views and opinions changed during these 12 years. One changing point for many Christians was the Euthanasia program (T4) which was strongly opposed even by some Church officials who previously had openly and strongly supported Hitler.
So, in the end you could end up with people like Heinz-Eduard Tödt who was awarded the Ritterkreuz in the Wehrmacht but was also a professor of theology and who struggled with his idea of faith, his service for the regime, his Churches' idea of duty and the horrors of war.
After the war the Church was not always self critical but there were noteworthy bishops and Christian organizations that were self critical about their role in World War 2 and Hitler Germany, some doubts were already raised in 1946 and 1948 and some of them even acknowledged the responsibility in the Holocaust very quickly.
And this of course meant that the protestant Church in GDR in the 1980s was a very different organization than in 1933. Their self understanding was pretty far away from getting Hohenzollern back on the throne.
The peace movement (Schwerter zu Pflugscharen) or loose organisations like Kirche von Unten were also rising up in the light of 40 years of the very discrimination that the Churches were afraid of in the 1920s and 1930s - though certainly different in quality between Stalin and Walter Ulbricht. For example the Protestant Church sometimes existed in a kind of almost limbo in GDR. Of course the Stasi had their eyes on them, but especially in the larger cities pastors could offer spaces for free discussions or "subversive" youth movements and musicians within the Church buildings which lead to interesting situations like Punk concerts in Churches in Berlin Prenzlauer Berg.
But even here you probably need to differentiate between different factions within the Church.
Sources:
Lutz Lemhöfer, Gegen den gottlosen Bolschewismus - Zur Stellung der Kirchen zum Krieg gegen die Sowjetunion, published in "Der deutsche Überfall auf die Sowjetunion" By Gerd R. Ueberschär and Wolfram Wette, 1991
Heinz Havemeister, Ronald Galenza, WIR WOLLEN IMMER ARTIG SEIN Punk, New Wave, HipHop und. Independent-Szene in der DDR 1980–1990, 2010