First of all, a bit of terminology. "Rabbinism" isn't really a thing. "Rabbinic Judaism" is, but from roughly 1000 years ago until present the overwhelming majority of Judaism has been Rabbinic (Karaites have existed and still do, but after 1000CE they were only a significant minority of Jews in a few regions). So, you're just asking about Judaism, full stop.

If you're looking for specific changes instituted because of the Holocaust, you won't find a whole lot. There is a field of "Holocaust theology", theology specifically dealing with the Holocaust, but it is not something the average Jew has necessarily been aware of or interested in. There are communities where Holocaust remembrance day, Yom HaShoah, has been given particular religious significance. It is a civil memorial day in Israel, but there are people who observe it as a fast day and do various rituals for commemorating other bad days on the Jewish calendar, but it is a very small-scale practice for a variety of reasons. For the most part, people commemorate Yom HaShoah as a memorial day, and in a religious context just think about the Holocaust on other days on the Jewish calendar reserved for mourning historic calamities.

In terms of general changes to the Jewish world, the effects have been immense. Eastern Europe was a huge center of Jewish life, which was almost entirely destroyed. The Rabbinic centers of gravity moved to America (which had been a Jewish, and especially a Rabbinic backwater a few decades before) and Israel. Yiddish ceased to be a powerful Jewish language. Before the war, German Jews fleeing the Nazis formed an important part of Israeli demographics. After the war, American Judaism got a major boost of Eastern European traditional Jews who had not had the assimilation/"melting pot" experience of the past few decades in America. I've seen it argued (though I'm not sure I agree) that the explosive growth of widespread intensive Jewish learning among Orthodox Jews was in large part driven by a desire to replace the centers of religious scholarship that the Holocaust destroyed.

The Holocaust changed the Jewish political scene, too. Bundism, which was a major Jewish ideology before the war, was effectively crushed by the one-two punch of the murder of most of its adherents, and the lack of a large enough Jewish minority in Eastern Europe to be meaningful politically. Zionism had a large core of adherents relatively unharmed in Israel, and the experience of the Holocaust made it a compelling ideology for Jews abroad, too. Before the Holocaust Zionism was a major political force among Jews, but a definite minority, opposed by most of the traditionalist world (who were uncomfortable with the nationalism) and most of the secularist world (who were uncomfortable with the particularism, and preferred socialism in their home countries or assimilationism). After the Holocaust Zionists were able to persuasively argue to both secularists and traditionalists that a Jewish safe haven had value, even if various elements of Zionist ideologies were uncomfortable.

And of course political support for Zionism was significantly raised after the Holocaust, which was an important factor building support for Israel, which in turn influences basically all of Jewish history in a variety of ways in the past 70 years or so. That includes communities who were not directly affected by the Holocaust, whose history was indirectly altered by it that way. Mostly I'm referring to the early-50s mass migration of Middle Eastern Jews to Israel, which affected Israel's demographic makeup and effectively ended Jewish life in areas which previously had substantial and long-term Jewish minorities (this time, thank God, not because they'd been killed). Those places, such as Syria, Iraq, Yemen, and Egypt basically had their entire Jewish population migrate in a short time span. Of course it's impossible to say what would've happened without the Holocaust regarding Israel and the Middle East, but nonetheless those communities were indirectly affected despite not being targets of genocide (with the exception of some Jewish communities in North Africa).

So in terms of hard religious changes that the Holocaust brought about, the list is pretty bare. But the disruption of such a major center of Jewish population had major impacts to the Jewish world, and the demographic impact that many Jews being killed and the survivors moving around had is a major part of the Jewish landscape today.