How did the destruction of the temple at Jerusalem affects relations between Jews and christians?

Answer 1

With the destruction of the Temple, Judaism shifted from being a Temple-centric religion to a synagogue based religion. As what happened with the destruction of the First Temple, prayer replaced sacrifice with the destruction of the Second Temple.

Answer:

The above answer is based upon a common misconception. Jews always prayed in synagogues, even when the Holy Temple stood. Even within the Temple premises, there were several synagogues. During the Second Temple era, ancient Greek authors attest to the large synagogues that stood in all the countries where Jews lived. The Dioploston in Alexandria, for example, was famous for its size (Talmud, Tosefta Sukkah 4:6). In First Temple times also, synagogues served the same function that they do today (Talmud, Megillah 26b and Berakhot 31a).

To answer the original question, after the Destruction, prayer (which had always existed) would now be the sole offering to God, alongside the Torah-study and performance of mitzvot (Torah-commands).

In addition, there are a number of commands (relating to the sacrifices) that we would be unable to perform.

Also, the Sages took several steps after the Destruction: they recorded the Temple-procedures in Talmud tractates such as Shekalim, Yoma and Tamid, and they enacted observances to remember the Temple (Talmud, Sukkah 41a) and mourn its destruction (Talmud, Sotah 49a).

The Second Destruction, as painful and tragic as it was, at least accomplished the disappearance of the impious cliques (as alluded in the parable in the Talmud, Gittin 56b, in which the "barrel of honey" represents the Temple, and the "דרקון" hints to the Sadducees, among others). Once the Temple, and Jerusalem, were razed, the men of power melted away and the internal life of the Jewish communities returned to the aegis of the Torah-sages. Other non-traditional groups such as the Samaritans and the Essenes also now dissociated themselves from the Jewish people.

Answer 2

At the time of the Destruction of the 2nd Temple in the year 70 CE, there was no relations at all between the Christians and the Jews. At that time, The Christian church had not yet formed, and the New Testament had not yet been written.