How did the destruction of the second temple in 70 CE affect the ride of Christianity

How did it strengthen Christian claims? How did it render rabbinic piety a practicable alternative to temple worship?

I don't think it strengthened Christianity in any way. But rabbinic Judaism as we know it was at a pivotal juncture there. The Jewish people had a strict set of laws, on for every bone in the body (although they were off by one, as modern science reveals) and now there were many of them that could no longer be followed. The rabbi's, which came out of the efforts of the Pharisee's, had the difficult task of holding the Jewish faith and people together, if not for them, it would most likely have died out.

it was 70AD and it was the beginning of the curse the lord had put on Israel as stated in Deuteronomy 28 chapter.

Persecution fired up the Church. Exodus 20:8-11
SDA