G-d describes Himself in His Torah as "a jealous G-d" (Shemos 20:5). He forbids us to display any interest in any other religion (Shabbos 149a). We are not permitted to attend a religious service of any other faith, or even watch it on television (see Nefesh HoRav pg. 230). We may not study works of or about any other religion (Rambam Hilchos Avodah Zarah 2:2), watch films about them, or study any pieces of religious art. A Jew may not enter a house of worship of any other religion even during the hours that services are not being held[1]. We may not even "utter upon our lips" the name of any other god (Shemos 23:13). This jealousness of G-d is not because He feels personally slighted and hurt. Tehillim (2:4)[2] described G-d as sitting in heaven and having himself a good chuckle over all idolatrous practices. But the concern is rather that these practices have a negative effect on mankind[3].
We may not donate any funds towards the furtherance of any other religion (Avodah Zarah 13a), nor advise or help in any other way to maintain any other religion.
It is well known that certain religions encourage their clergy to engage in dialogue with the Jewish clergy in order to further conversion[4]. It is obvious that we may not aid the clergy of any other faith in furthering their religion in such a fashion, or in any other fashion.
The mere comparison of the Jewish religion with any other religion already constitutes an affront to the Jewish G-d, as if to imply that there is something substantial shared in common between the two. Rambam (Iggeres Taiman chapter 1) compares this to a real person standing next to a statue of a human being, and having someone compare the two.
Each religion is defined by its principles of faith. Judaism is not a "twin sister" to any other religion. Even Catholicism, which started as a break away from the Jewish religion, has moved over the centuries so far away from Judaism, it is improper and misleading to speak of any "Judeo-Christian tradition". Even when these two religions share the same positions on certain moral and ethical issues, the source of the binding force for each group of adherents is totally different.
The Holy Temple represented the notion of the chosenness of the Jewish people. The "western candle" of the menorah burned miraculously to indicate that G-d chose to dwell only with the Jewish people (Shabbos 22b). The twelve loaves that sat on the shulchan all week long were miraculously still fresh and warm at the end of the week, to show how beloved the Jewish people are to G-d (see Chagiga 26b). The keruvim hugging each other represented the idea that G-d loves His chosen people like a husband loves his wife (Yuma 54a). According to Talmudic tradition (Bava Basra 99a), at the time the Jews were not properly observing G-d's Torah laws the keruvim would not even be facing each other. Nonetheless, at the time the enemies entered the Holy Temple to destroy it, they noticed that the keruvim were hugging each other (Yuma 54b). At first glance this doesn't seem to make sense. Wasn't the destruction of the Temple due to the fact that the Jews were not keeping the mitzvos? How could it be that at that time the keruvim were looking at each other, let alone hugging each other[5]? The explanation for this is that G-d did not want the enemies to think that at the time of the destruction of the Temple the Jews had lost their status as "am hanivchar". Even at the time that G-d shows his smiling face to the other nations of the world ("af chovev amim") and delivers the Jews into their hands for punishment and torture, we still maintain our status as "am hanivchar" ("kol kedoshav beyadecha")[6].
G-d singled out the Jewish people and chose to love them as "a daughter", "a sister", "a mother", and "a wife"[7]. The relationship between husband and wife after nisuin is considered much stronger than any other relative. The husband unites with the wife - in nisuin - to be considered "baal davar"[8]. During erusin the wife is considered an eshes ish who is not yet bevies habaal. Nisuin consists of hachansa lershuso for the purpose of completing the ishus. The woman then becomes an eshes ish bevies habaal. The concept of beiso zu ishto applies only after nisuin (Yuma 13a). The Holy Temple is "beis Hashem", and when the Jewish people entered the temple their nisuin with G-d was completed. The luchos were the kesef kiddushin to create the erusin[9], and the building of the mishkan made it possible to have the nisuin. The Rabbis had a tradition[10] that this is what was referred to in the posuk in Shir HaShirim - the fact that the Jewish people coronated G-d on the occasion of their marriage which started with the luchos and was completed with the building of the mishkan.
After the destruction of the first Temple many Jews assumed that since the marriage abode was just destroyed, apparently the marriage was terminated; the Jews were no longer the chosen nation and there was no longer any sense in keeping mitzvos (Sanhedrin 105a). G-d sent His prophets to notify His nation that the marriage was not - and never will be - terminated. The bechira of the Jews was of an everlasting nature.
When the prophet Yechezkel told the Jewish people about the upcoming destruction of the Temple, he added that G-d would still maintain - in Bavel - "a miniature Temple" (11:16). This was to indicate that despite the churban they had not lost their chosen status. According to the Talmudic tradition, this refers to botei knesios and botei midrashos all over the world (Megilla 29a).
After the destruction of the second Temple a sect of non-Jews developed a similar theory, that the Jewish people had lost their status of "am hanivchar"[11]. Ever since the beginning of the Zionist movement, that very same group has consistently expressed its view that since Eretz Yisroel is the "chosen land", specially reserved for the "chosen nation", the Jews were therefore not entitled to that land[12] because they had lost their status as the "am hanivchar"!
The consistent insistence of certain sects to internationalize the old city of Jerusalem stems from this same position. Our acquiescing to such demands would imply to those groups our admitting to their position, which is in total contradiction to this fundamental principle of our faith. The chosenness of our people is everlasting, even during and after periods of churban.
When King Solomon built the Temple, he welcomed non-Jews to come to pray (Melochim I, 8:41). But only provided they came "for the sake of your name"; and only provided they subscribed to the concept of "bechiras Yisroel", which the Temple represented. A non-Jew who does not believe in the Jewish G-d, or who does not recognize our status as "am hanivchar", is not invited to come.
Just as King Solomon only welcomed to the Temple in Jerusalem those non-Jews who accepted the Jewish G-d, and who recognized the chosenness of the Jewish people, so too in our botei kneses and botei medrash we only welcome such individuals.
The prophet Yeshaya also speaks about the time the Temple will be rebuilt and sacrifices will be brought by non-Jews, because "my Temple is a house of prayer for all the nations" (56:7). This, of course, is only provided that their prayers and their sacrifices are directed towards the Jewish G-d, and that they recognize bechiras Yisroel.
The rabbis had a tradition that when Titus destroyed the second Temple, he was merely grinding flour that had already been previously ground[13]. The idea contained in that tradition is that the non-Jews really don't have the ability to defile holy sites. It must be that the Jews had already sinned to such an extent that - in a spiritual sense - the Temple had already been destroyed, and there was really very little defilement left for Titus to accomplish[14].
Similarly tradition has it that if a beis hakneses or a beis hemaedrash is defiled by adherents to some other religion, it probably was due to the fact that the Jews who were using that beis hakneses for prayer, or that beis hamedrash for studying Torah, were not acting with the proper derech eretz for such a holy site[15].
The sanctity of the Temple was clearly on a much higher level, and required of us to demonstrate "morah hamikdosh". The sanctity of the "miniature Temples" is on a lower level, and therefore only requires of us "kvod beis hakneses". But still it is expected of us that our deportment in botei kneses and botei medrash be of such a nature that it should reflect this principle of bechiras Yisroel.
[1] See Shulchan Aruch Yoreh Deah (end of siman 157)
[2] See Rambam in Iggeres Taiman
[3] See commentary of Rav S.R. Hirsch (end of Parshas Emor)
[4] See N.Y. Times Sept. 23, 2000 (pg. A8)
[5] See Ritva and Maharsha
[6] See Rashi to Vezos Habracha(33:3)
[7] See Rashi to Shir Hashirim(end of chap. 3)
[8] See Rosh to Makos (end of chap. 1) quoting Ravad
[9] See Nefesh Horav (pg. 289)
[10] Last Mishna in Taanis (26b)
[11] See Chagiga (5b) and Yad Haktanah
[12] See Mipninei Horav (pg. 109)
[13] See Sanhedrin (96a) and parallel Midrashim
[14] See Mipninei Horav (pg. 205), and Nefesh Hachayim
[15] Mishna Berura (siman 151, nos. 1and 2)