It's interesting to compare and contrast Christianity and Islam.

Christianity originated when its founder, a religious reformer, was killed.

Islam originated when its founder, a religious reformer (and self-proclaimed prophet), died of natural causes after having united almost all the Arab peoples into one hell of a fighting force that quickly conquered most of the world from Spain to China.

Jesus' messaging includes statements like "Render to Caesar the things that are Caesar's...." This is a reminder that early Christians were persecuted by the Jewish rules and later, to some degree, Romans (though Roman persecution is way overhyped). Many Christians have a mentality of identifying with the downtrodden, the persecuted, those outside of power, etc.

Islam, to the contrary, does not have this same emphasis on self-preservation in the face of hostile political or religious organizations. Islam, during the time of Muhammad, militarily defeated his opposition! Thus some of the gravest crimes in Islam are related to apostasy and turning away from Islam (historically apostasy was a death penalty crime, and it still is today in some countries).

Without getting too long winded, yeah, I think there's an old strain of Christianity that DOES focus on the "turn the other cheek" (and not the rest of the quote), the "render unto Caesars" and the "blessed are the poors."

And, to be fair, Islam and Christianity share an awful lot in common in terms of moral teaching. THere's a big emphasis on charity, helping the downtrodden, etc.