The words "Sheheim Mishtachavim Li-Hevel Voryk Umispallelim El Eil Lo-Yoshiya" - Was this originally part of Aleinu and then removed, or was it added later to Aleinu? Why was this done?
וּמִצְרַ֕יִם הֶ֥בֶל וָרִ֖יק יַעְזֹ֑רוּ לָכֵן֙ קָרָ֣אתִי לָזֹ֔את רַ֥הַב הֵ֖ם שָֽׁבֶת׃
הִקָּֽבְצ֥וּ וָבֹ֛אוּ הִֽתְנַגְּשׁ֥וּ יַחְדָּ֖ו פְּלִיטֵ֣י הַגּוֹיִ֑ם לֹ֣א יָֽדְע֗וּ הַנֹּֽשְׂאִים֙ אֶת־עֵ֣ץ פִּסְלָ֔ם וּמִֽתְפַּלְלִ֔ים אֶל־אֵ֖ל לֹ֥א יוֹשִֽׁיעַ׃
As Wikipedia writes, it was a base for accusations against Jews since the 14th century, even though the words of Yeshayahu far predates Christianity and almost all researchers agree that the first part at least was composed no later than the Second Temple era.
Both the date of incorporation to our daily prayers and the censorship is a matter of debate. Aleinu can be found at the end of the weekday shacharit in Machsor Vitry, this particular copy of the British Library is from around 1242 and it is there in earlier copies. However, in another manuscript from the 14-15th century stored in Cambridge it is still written and later censored. It is most probable that the censorship happened around the 15th century, as Jewish Encyclopedia suggests, earlier than the 1703 Prussian incident.
This is further confirmed by some old prayer books. The earliest example that I've found on HebrewBooks is a siddur from Bologna, 1540. Here the sensitive parts are omitted by inserting two blank spaces:
...שֶׁהֵם מִשְׁתַּחֲוִים (...) וּמִתְפַּלְלִים (...) וְאָנוּ כּוֹרְעִים
...שֶׁלֹּא שָׂם חֶלְקֵנוּ כָּהֶם וְגוֹרָלֵנוּ כְּכָל הֲמוֹנָם (...) וַאֲנַחְנוּ כּוֹרְעִים
Those words were removed following a decree by Frederick I of Prussia in 1703