The question has been posed by a curious atheist: "Would it be possible to come up with an atheist compatible Jesus?". I would say that the answer for the most part is yes, but at the same time ask whether it would really be worth it. The answer to that counter-question largely depends on what the atheist's real goals are.
The major difficulty is that every record we have of Jesus' words and deeds suggest that during his public ministry he claimed to be the Son of God. This, obviously, is right out compatibility-wise if the goal is to retain a picture of Jesus as a good or wise teacher. A man who goes around claiming to be the Son of God and isn't would have to be a fool, a deranged man, or a con artist. Obviously any Jesus who was one of these three types would be compatible with atheism. But he would not be anyone worth emulating.
Those who want to retain the positive contributions they feel Jesus made to the ethical and spiritual realm can argue that these claims to divinity must have been added by later Christians. This undertaking is what you see today in dozens of books found in the Christianity section of your local bookstore. There one can find arguments that Jesus was a Cynic philosopher, a political revolutionary, or just about anything other than the Son of God. The soundness of these arguments and the validity of their authors' methods are best left for other nodes; enough to say that they have not proven entirely satisfactory for many.
And there's one problem for atheists that just doesn't go away. Whether he claimed divinity or not, he at the very least was a devout Jew who himself believed in God. The overwhelming likelihood is that he considered himself a participant in a special covenant made between God and the people of Israel. Whatever other influences may or may not have been there, his ethics and spirtuality would have been deeply rooted in these beliefs. An admiring atheist would have to admit that he nevertheless considered Jesus' outlook on life, the universe, and everything to be based on a colossal error.
But if we were to grimly press on, and strip away all the God-business from our Jesus, what would we be left with? Not much, methinks. Many of his declarations are ridiculous when the underpinnings of a Judeo-Christian cosmology are removed. The meek will certainly not inherit the earth. Collaborating with an oppressor by voluntarily extending a forced march of one mile into two becomes a contemptible act. Loving your neighbor as yourself sounds good as long as your neighbor is a relatively decent sort, but Jesus demands that you love awful, terrible people who hate you and want to kill you. We're left with a moral teacher whose teachings become either nonsensical or so watered down that one would be better off turning to the secular philosophers.
In which case one has to wonder what the point is. The atheist who undertakes this project has to find something undeniably compelling about the man to jump through as many hoops as these in order to keep him in their life. I would suggest that this person ought, for honesty's sake, to seriously consider whether their program shouldn't consist of fitting Jesus into their worldview, but fitting themselves into his.
Or it could be just one part of a larger program. Wavering Christians might be successfully lured away from their faith toward an atheist worldview made more acceptable to them by hanging a Jesus on it. For instance, if what Jesus really cared about was helping the poor, then anything you think might help the poor could be presented as being compatible with Jesus' "true" mission--even if it utterly conflicted with Christian principles.