I agree that existentialism needn't correspond to conventional morality. Indeed, existentialism can be as radical as Jesus's counterculture.
You seem to be leaning towards the liberal take on Jesus, which reduces his vision to one of basic morality. We should "care about others," in which Christianity is just an outgrowth or a validation of the basic social instinct.
On the contrary, though, this basic morality is unnatural and anomalous. The animal instinct is to care about ourselves and those we select as our kin (our friends and family), not about the abstraction of "humanity." Jesus's morality was absolute and therefore (purportedly) otherworldly. Moreover, Jesus seems to have understood how hard it is to practice those moral absolutes, which is why he stressed, as I pointed out, that the first will be last and the last first. Those who succeed the most in earthly terms will end up in Hell because our natural instincts are demonic. God is transcendent, which means the powers that rule over nature are sub-divine.
Anyway, this radicalism meant that Jesus's morality promoted a counterculture of insider absolutists. Most people aren't Christ-like, which is why organized Christianity had to dilute the message to save the face of the average Christian. Supposedly, Jesus did all the work on the cross, so Christians need only trust in Jesus to be saved.