Islam maintains that Jesus was a prophet, and a true and great prophet. However, his later followers distorted his message and said that he died and rose again from the dead as an atonement for sin, and that he was the Second Person of the Triune Godhead. According to Islam, God would never permit one of his True Prophets to die a criminal's death, and so they consider the Christian doctrine of crucifixion to be a sacrilege against Jesus.
Atheists, of course, think that Jesus had no supernatural powers (since for them nothing supernatural even exists), but many of them do think that Jesus lived and died on the cross. Of course they deny a resurrection, since that would have to be supernatural. My ex-housemate Keith Parsons, who is an atheist philosopher at the University of Houston at Clear Lake, thinks that Jesus was crucified, dead, and buried, and that the disciples hallucinated the risen Jesus and founded Christianity. Other atheists sometimes assert the Jesus Myth thesis, that Jesus never even existed and was made up by the early Christians. I think this is still a minority position even amongst atheists.
But Christians, Muslims, and atheists can all agree on this: that either Jesus died by crucifixion or he did not die by crucifixion. Whatever position you take on that matter, you can be either right or wrong. You can't be both or neither.