"Is it absolutely essential that people believe in the fictional concept
of "property rights" in order to interact productively and peacefully?"
"In the real world, yes. Numerous groups have tried to eliminate property
rights to create this wonderful utopia, and have pretty well proven that it's impossible."
Just as you can't peacefully take something from a child when the child thinks they own the object, you can't "eliminate property rights" when people still believe in the fiction. As long as people honestly believe there is not enough for everyone, they will try to hoard as many resources for themselves as possible. The concept of property rights justifies this hoarding. Of course, this collective hoarding behavior, caused by the belief that there is not enough for everyone, creates the situation where there is, in fact, not enough for everyone and further reinforces the belief and the hoarding behavior.
In the real world, though, there is an abundunce for everyone. One of the main reasons that people aren't enjoying this abundunce is that they continue wasting their time maintaining conflicts and divisions among themselves. Another reason is that people waste their time reinforcing dominance relationships. The classic example of this is the current school system, in which children waste most of their childhood learning how to be obedient and subservient rather than learning how to actually improve their own minds and lives.
Mark, from your statement, I am unsure whether you believe that a wonderful utopia has been proven impossible or whether you believe that it is impossible to attain utopia by forcing people to stop living by the concept of property rights. It is popular to believe that utopia is impossible because it justifies giving up on happiness and settling for misery, which those who would dominate you would rather have you do and have taught you this from the beginning. Of course, forcing people to stop hoarding property only creates more conflict and less desire for people to work together peacefully.
I recognize the fact that people are much more intelligent, creative and prosperous when they work together peacefully. Whether they believe in the concept of property rights is as irrelevant as whether they belive in Santa Claus. I view "property rights" as basically a truce between fundamentally violent, contentious people that they will refrain from taking that which the other "owns". As a diplomatic ploy, it has been somewhat successful.
However, if people did not continue maintaining traditions of conflict and dominance and if they had some basic respect for each other, they would simply have no desire to take that which another is currently using, since they would not want to create a conflict between others and themselves. They wouldn't need the psychological crutch of "property rights" to maintain a civil, productive society.