The answer to this question depends on which of the three – now two – successor states of Nazi Germany you are talking about: The Federal Republic of Germany (West Germany), The German Democratic Republic (East Germany), or Austria. And while these three different societies as well as now unified Germany had and have different relationships to the Nazi past as well as to anti-Semitism, what they all share in common is that anti-Semitism never really went away – something even apparent by recent election campaigns in both countires.
To use some of the most obvious examples: In Austria anti-Semitism was frequently employed in political discourse with the most egregious examples being the Kreisky-Wiesenthal Affair and the Waldheim Affair.
Concerning the Kreisky-Wiesenthal aka Kreisky-Peter-Wiesenthal Affair: Being extremely wary of another but still forced to come together to form a government, the Social Democratic Party and conservative party of Austria were throughout the 50s and 60s constantly searching for ways to be rid of the other. In 1966, the ÖVP managed to rule not in a coalition but alone and as part of the backlash, the SPÖ was determined to take back power. Enter Bruno Kreisky. Kreisky, a Social Democrat from a Jewish family had fled Austrofascism and Nazism to Sweden in the 1930s and returned after 1945 to become of the leaders of Austrian Social Democracy. In 1970 he engineered a pivotal political move in Austrian politics: The SPÖ went on to rule despite not having the required majority in parliament to pass laws. This was only possible because the FPÖ [Freedom Party of Austria – the party of former Nazis] under Friedrich Peter, a former Waffen-SS and Einsatzgruppen member, were willing to support his government. A year later, the SPÖ called for another election and managed to gain 50%+ of the vote, unprecedented for them.
When in 1975 another election came around and the SPÖ feared for losing their majority, Kreisky started striking a deal with Peter: If the SPÖ lost the majority, they would rule with the FPÖ and Peter as vice chancellor. Around the time this was negotiated, Simon Wiesenthal, a Jewish Austrian Holocaust survivor unearthed details about Peter's past as part of an Einsatzgruppe as well as similar details about several SPÖ ministers in Kreisky's cabinet. This became a state affair with Kreisky going so far as accusing Wiesenthal to have a been a Gestpo spy during his time in the camps (a rumor manufactured with massive help from previous Austrian president Heinz Fischer, who was Kreisky's secretary) as well as defending Peter.
The affair became a pivotal moment for the question of how Austria dealt with its Nazi past and that Kreisky, a Jew in the eyes of a lot of Austrians, defended Peter against another Jew, Wiesentahl, coupled with a massively anti-Semitic campaign of the FPÖ against Kreisky confirmed to many in Austria that Nazis were an ok part of Austrian society while on the outside, it furthered Austria's image as a Nazi country. It also saved the FPÖ from disappearing from the political scene since the affair lead to a renewed surge of voters for them.
About ten years later, the same anti-Semitism that had driven the anti-Wiesenthal campaign in Austria manifested itself again in the so-called Waldheim Affair. In 1986 former UN general secretary and Austrian diplomat Kurt Wladheim ran for president in Austria. During his campaign, various news outlets unearthed details about his Nazi past. Waldheim had been part of the SA (the horse riding corps) and had served as an intelligence officer in the Balkans in the Wehrmacht, an area where it was known that people like him were frequently involved in Nazi war crimes. Waldheim denied everything and claimed "he had only done his duty". This not only lead to the joke that only his horse had been part of the SA (with opponents of Waldheim displaying a wooden SA horse all around Austria ) but also to a massive backlash against these revelations.
This backlash resulted in Waldheim not only putting out posters saying "Now more than ever" but also to a media campaign that charged that Waldheim's past was only brought up as a conspiratorial ploy to make Austria look bad by the frequently cited "certain circles on the East Coast [of the US]", which functioned as a barely veiled dog whistle for Jews. Amid this revanchist and anti-Semitic media and political campaign, Waldheim was indeed elected.
But such occurrences were hardly contained to Austria. In the Federal Republic of Germany, the immediate years after the end of WWII saw a huge number of anti-Semitic occurrences and attacks. According to three studies conducted between 1946 and 1952, one third of the German population showed strongly antisemitic attitudes, while another third exhibited partially antisemitic tendencies. The younger generations, molded by their experiences during the Nazi period, were found to be most stridently antisemitic.
This often manifested violently, especially against Jewish Displaced Persons living in camps all over Germany and waiting for repatriation or emigration to the US, the UK, and Palestine/Israel. In 1946 180 German police men conducted a raid on a DP camp in Stuttgart during which they shot one camp survivor and injured another three; in the Föhrenwald DP camp during a raid by the financial authorities, the German bureaucrats angered the DPs by shouting "the gas chambers are waiting for you!". Furthermore, the post-war years in Germany saw a massive wave of destruction of Jewish cemeteries with literally hundreds of recorded incidences. When Veit Harlan, director of the anti-Semitic Nazi film classic "Jud Süß" was put on trial in the early 1950s German newspapers were full of letters to the editor spewing anti-Semitic rhetoric and there were anti-Semitic riots in several German cities. At the same time, German state officials such as the mayor of Offenbach denied Jews employment. And one of the parties that saw itself as the successor party to the NSDAP, the Socialist Reich Party, was elected into several state parliaments before it was outlawed in 1952.
However, towards the end of the 1950s several incidents occurred that shocked German politicians, the German and international public to such a degree that the public-political attitude towards anti-Semitism began to change. Not only had Germany at the time seen a series of attacks on synagogues in various cities, including in Köln and Düsseldorf but had also experienced what is known as the "Zind case". The Zind case revolved around Ludwig Zind, a Studienrat (civil servant position in German schools) and former SD member form Offenburg. On the night from April 23 to 24, 1957 Zind quarreled with a man named Kurt Lieser in a restaurant in Offenbach called Zähringer Hof. During the quarrel, Zind belittle Lieser, who was a Concentration Camp survivor, with anti-Semitic remarks, blamed the Jews for the decline of the Weimar Republic, justified the Nazis killing Jews, and boasted to Liser about how many Jews he had killed during the war. He also told Lieser that it was a pity that he wasn't gassed by the Nazis.
Lieser reported Zind to his superiors who when they talked to him found Zind unwilling to retract what he said or apologize for it, claiming further that Israel and all Jews ought to be eradicated and so forth. With no apparent consequence for Zind from his superiors, Lieser then informed the German magazine Spiegel, which published a widely read article about Zind. After the publication of the article, the Public Prosecutor in Offenburg started investigation against Zind that ended in an indictment for slander and violating the memory of the dead. Zind was convicted but before being transferred to jail, he managed to escape, first to Egypt and then to Libya, only to be arrested years later in 1970.
The case Zind was a shock to the Federal Republic. When in its wake over 700 attacks on Jewish institutions followed, the German government decided to take decisive steps. Not only did German politicians henceforth start speaking up strongly against anti-Semtism, the Federal Republic even changed their laws by introducing §130 to criminalize incitment to hatred, including anti-Semitism and Holocaust Denial.
Since then, public attitudes in West Germany have changed towards anti-Semitism. By the end of the 1980s, only 5% of the West German population was blatantly, and over 15 % considerably, anti-Semitic, which is in line with Western European averages. East Germany has its own history with anti-Semitism which is long and pronounced but suffice it to sum it up as the GDR following the Stalinist of anti-Jewish campaigns in the 1950s to the 1980s when the East German state made a conscious effort to be on good footing with its Jewish communities and combat anti-Semitism.
All these numbers and campaigns however did not mean that anti-Semitism simply disappeared in West or unified Germany. The 1980s saw the spectacular fall of Ernst Nolte from respected historian to Holocaust Denier, the Bitburg Affair etc. while the 90s were marked by anti-Semitic campaigns against the Wehrmacht exhibition and Martin Walser's speech on Auschwitz and even the 2000s were marked by debates surrounding MP Hohmann's remarks on the Jews and the Möllemann Affair. So, while there was a noticeable point at which West German public debate on anti-Semitism changed, it certainly did not clear up in Germany.
Sources:
Werner Bergmann: Antisemitismus in öffentlichen Konflikten. Kollektives Lernen in der politischen Kultur der Bundesrepublik 1949-1989. 1997.
Peter Reichel: Vergangenheitsbewältigung in Deutschland. Die Auseinandersetzung mit der NS-Diktatur in Politik und Justiz. 2001.
Christoph Nonn: Antisemitismus. 2008.