Aleynu: A Controversial Prayer

Many different sects within Judaism have eliminated various verses in the prayer over time. Many Ashkenazi and Reform prayer books have removed the verse “la-hevel va-rik” (vanity and emptiness), because its numerical connotation equals that of Jesus and Muhammad. For centuries Jews in Eastern Europe were attacked by the Church if caught reciting this verse in the Aleinu prayer. However, most Sephardic and Israeli siddurim leave this verse in the Aleinu. Additionally, nearly all Reform congregations have eliminated the verse “for God has not made us like the nations of the land.” During the establishment of the Reform movement, many Jews sought the complete integration of the Jewish people into their mother country. This verse was extracted as a result of the proclamation that the Jewish people were the “Chosen People” and unlike other citizens. In the Diaspora, Jews did not want to be singled-out in society, merely because they were Jews.
--https://www.jewishvirtuallibrary.org/aleinu

Originally the text read that God has not made us like the nations who "bow down to nothingness and vanity, and pray to an impotent god." ... In the Middle Ages these words were censored, since the church believed they were an insult to Christianity. Omitting them tends to give the impression that the Aleinu teaches that we are both different and better than others. The actual intent is to say that we are thankful that God has enlightened us so that, unlike the pagans, we worship the true God and not idols. There is no inherent superiority in being Jewish, but we do assert the superiority of monotheistic belief over paganism. Although paganism still exists today, we are no longer the only ones to have a belief in one God.
--Rabbi Reuven Hammer, Siddur Sim Shalom (Conservative)