In my experience the "it was written by people who never met each other" doesn't quite land because the retort is "well how did prophecy all line up then?" suggestive stare

I find it's more useful to show Christians the weak point of the New Testament from their respective political view..

To left leaning:

Jesus told individuals to personally decide to give to the poor, he never instituted a state wide obligation, he never called for the church to force taxes from the unbelieving. He also condemned "porneia" (typically translated debauchery) which meant unlawful sex which at the time included homosexual acts.

To the right leaning:

Jesus said to turn the other cheek in the face of physical violence and threat. He said to surrender your possessions to anyone who asks and not expect it back (Luke 6:29-30). St Paul followed this saying it's preferable to be cheated out of money rather than sue someone (1 Cor 6:7)

Point being. Neither the left or right "own" Jesus. Nor does anyone else attempting to live a modern western lifestyle. It's incompatible. Jesus and his followers espoused radical self sacrifice. They believed the end was nigh. He said "give no thought for the morrow" because he didn't believe there were many left.