My dad told me the OP joke when I was a teen-ager. He thought priest-rabbi jokes were somewhat intellectual, in that one had to be conversant in two religions not our own (I was raised a Methodist.) Here are two more of my favorites:
A priest and a rabbi, whose houses of worship were across the street from each other, were talking one day and discovered each had need of a bus for various functions, but neither could afford one alone. They talked with their respective congregations and agreed to split the cost of a bus, with the proviso that it was to be utterly ecumenical – nothing on the bus would hint that it belonged to either congregation. Things went swimmingly until one day when the priest brought the bus back from a long weekend retreat and, after everyone had gone home, discovered that one of the parishoners had left her rosary on the bus. He absent-mindedly put it on the dashboard, intending to take it to the rectory with him, but forgot it. The next day, the rabbi went to use the bus, saw the rosary and decided that justice demanded that a Star of David be affixed to dash as well. The following weekend, the priest remembered the rosary, went to get it and found the star stuck to the dash. He grabbed the rosary and left; the following Friday evening, he parked the bus in front of the synagogue and, as the Jewish congregants left, stood in full regalia splashing holy water on the bus and loudly blessing it. Having made his point, he strode off. The next day, feeling contrite and ashamed, he went to apologize to the rabbi and talk things out. The rabbi’s secretary said he had gone to the garage where the mutual bus was parked. Puzzled, the priest went to the garage. He heard sounds of industry coming from under the bus, walked to the back, leaned down – and found the rabbi, busily sawing off two inches of tailpipe.
A priest and a rabbi car-pooled each Wednesdy to an ecumenical meeting in a nearby city and, during the drives, had many long conversations about religion. They became fast friends, and started teasing each other about the quirks of their respective religions. One day the rabbi joked, “You know, your Gospels make it clear that Christians are supposed to proselytize. Why don’t you try to convert me?” The priest took up the challenge, also in light-hearted manner, and they thus passed the hours of their commute week after week. This had gone on some time when one day both men got to laughing so hard the driver lost control of the car and it went off the road, rolling several times, throwing both men clear. Miraculously, neither was badly injured, but as the priest lay there on the ground gathering his wits, he saw the rabbi standing nearby, appearing to cross himself. “I did it!” the priest cried, jumping up. “I actually converted you!” To which the rabbi retorted, “Nonsense, I’m just checking to make sure I still have everything,” then proceeded to touch himself again, naming the items he was checking: “Spectacles, testicles, watch and wallet.”