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The answer by the impeccable u/kieslowskifan that u/abbot_x has linked to provides a good overview of the topic. I merely want to expand a bit on the dynamic behind some of the changes in how the issue was treated in West Germany particularly. Basically, while it became increasingly unrealistic that the eastern borders of Germany would ever resemble those of 1937 (i.e. before the Anschluss of Austria to Nazi Germany, think interwar Germany before Nazi annexations) again, the issue was kept alive in public debate in the Federal Republic. Most knew that bringing it up was beating a dead horse but spelling it out was deemed politically unwise for a long while.

As the others have already correctly pointed out, whatever the East German sentiments among party members or in the people might have been, the German Democratic Republic was in no position to bargain with the victorious Soviet occupiers who had decided on the western expansion of Poland as compensation for the Soviet annexation of eastern Poland (and German Königsberg, now Kaliningrad). Thus, the GDR was the first German state to accept the Oder-Neiße border when it formalized its diplomatic relationship with Poland in 1950. This was quickly denounced by West Germany who neither accepted the GDR regime as legitimate representative of German interests nor its agreements. During the 1950s and for most of the 1960s, the official position of the Federal Republic of Germany was clear: There was no conclusive agreement on the borders of Germany until it was properly re-unified (i.e. democratically) and a peace treaty between unified Germany and the Allied powers was signed, which had never been done in the aftermath of the German surrender. Instead, with the beginning of the Cold War, the occupation zones of the Western Allies and the Soviet occupation zone had gone separate ways, each coalescing into a German state, both not fully sovereign and each aligned with their occupying power bloc.

West German politicians of all political persuasions (except communist) vowed to never accept the post-war state of affairs: The undemocratic, Soviet-installed puppet regime that now ruled over 18 million Germans (and bloodily crushed a popular uprising with the help of Soviet troops in 1953) and the uncompensated expulsion of around 12 million Germans from the eastern territories lost in the war, of which the West took more than 8 million. The preamble of the 1949 West German constitution, the Grundgesetz, declared the constitutional arrangements of the Federal Republic to be provisional until democratic unification would be achieved. The Cold War had just begun and the two rival blocs were just taking shape. Germany’s place in this new world was not conclusively decided yet. At the time, no one knew how long the German separation would endure. Early West German politics treated the Oder-Neiße border in the same vein: A temporary arrangement that would hopefully be readdressed in the near future, ideally with a right to return by millions of refugees.

There was ample political reason to do so too. Over 8 million German Heimatvertriebene (how these German refugees were called) had to be distributed, housed, and fed across a war-torn country. But more than that, they represented a sizable voter bloc with a distinguishable political interest that could be pandered to by indignative Oder-Neiße rhetoric. Heimatvertriebene set up their own associations and lobbies and even political parties (the BHE), but they were also well-represented in both major parties, the Social Democrats (SPD) and the conservative Christian Democrats (CDU), the latter of which ruled the young Federal Republic from 1949 to 1968. Both political camps had their own reasoning for this too. The CDU fathered/mothered the West German project–the quintessential governing party–, the integration into the Western bloc, and its foundational anti-communism. With anti-Oder-Neiße rhetoric it could present itself as the indispensable guarantor of German interests vis à vis communist rule domestically, especially as Konrad Adenauer’s (CDU) administration managed to get the Western Allies to denounce the unauthorized agreements of 1950 between Poland and the GDR. The oppositional SPD on the other hand struggled to find its place early on in the CDU-run Federal Republic of the 1950s. Under its larger-than-life leader Kurt Schumacher, the Social Democrats rejected the CDU course of integration into the capitalist West as misguided and campaigned for a neutral unified Social Democratic Germany instead. Until their new Godesberg platform of 1959, the SPD tried to be somewhat of a left-wing nationalist alternative to the CDU-dominated post-war political consensus. I’ve written some more on that curious part of SPD history here. In this vein, the SPD tried to outdo any anti-Oder-Neiße rhetoric of its rival, accusing the Adenauer administration of giving up on the East for integration with the West.

Basically, because both major parties competed for their votes and both had their reasoning for border revisionism, Vertriebene had a somewhat outsized political sway in West Germany. At least as long as the memory of their lost homes was somewhat fresh on the minds of many Germans and as long as the German separation seemed temporary, the issue of Oder-Neiße stayed “hot” so to speak.

There is an answer by u/kieslowski fan that touches on this with respect to West Germany, which I'll supplement a bit here.

Basically, mainstream West German politicians didn't think Germany would actually reclaim the territory east of the Oder-Neisse line that had been awarded to Poland and the Soviet Union at Potsdam. There was no practical way to do it and America and Britain had agreed to the Oder-Neisse line, after all. But basically nobody in German politics was willing to actually and officially accept the Oder-Neisse line until after reunification.

This was mostly for domestic political reasons as detailed in the linked answer. The Federal Republic's self-concept was that it was the sole legitimate government in Germany and that until it was able to make a free and democratic decision on the matter, its borders were what they had been in 1937. The borders imposed after WWII had some de facto reality but were technically preliminary and lacked German consent, which could only be given after reunification. In addition, refugees from east of the Oder-Neisse line were a significant constituency, at least early on (something like 1 in 6 West German voters in 1950) so at least initially no party was willing to risk angering them by giving up on their homelands.

There were actual revanchist organizations and parties in Germany. At the time of reunification, Die Republikaner was such a party. There was some fear DR would do well in the 1990 Bundestag election (the first "all Germany" election since before WWII), since they had gotten a promising start in municipal and European Parliament elections. Concern about DR helps explain CDU/CSU chancellor Helmut Kohl's refusal to give assurances on the the Oder-Neisse issue in 1990. He wanted to limit DR's room to his right. DR ended up winning zero Bundestag seats. After reunification and the preservation of the CDU/CSU majority, Kohl was willing to accept the Oder-Neisse line on behalf of a reunited Germany.

In communist East Germany--the DDR--the border was regarded as a settled matter. In 1950, as required by the Soviet government, the DDR signed a treaty accepting the Oder-Neisse line. The Soviets had a bigger army in East Germany than the East Germans did, so there was no real possibility of defying the Soviets on this point. There were some refugees in the East but most were in the West, so this was also arguably not as significant a domestic political issue, not that the DDR was at all democratic.