Despite the fact that the Levites were a priestly class, the Passover meal is partaken by all in the Jewish household. There are years when we have non-Jewish guests at our Passover Seder, and they freely eat along with us, even participate by performing some of the rituals that occur during the meal. No one is excluded. So it is very peculiar the way the Jehovah's Witnesses have done things with their Memorial observance.
What many people do not realize is that the Passover has pagan roots, likely from the family of Abraham before he was called by God to the Promised Land, even before Abram knew of God. We Jews, however, do understand this, and we view the Biblical narrative in Exodus as reflective not merely of the past days when we were slaves in Egypt, but through the lens of our time in Babylonian exile. The Exodus account is where "allegory constitutes a form of historiography" in which the Jews in Babylon reflected on their traditional history of once being slaves in Egypt and retold it using themes based on being separated from their home in the Diaspora, hoping to be reunited to their Promised Land again.
As The New Union Haggadah states: (the book Jews follow on Passover night to direct them though the Seder is called a "haggadah" for those who are unfamiliar):
What is described in the Passover story should be considered a veiled depiction of Jews displaced to Babylonia and eventually through the Levant after the conquest of Jerusalem in 586 BCE....They had to invent a new paradigm of peoplehood and leadership...In exile, Moses encounters God not in a sacred Temple or an otherwise renowned holy site, but in a lowly bush. The experience transforms him, as will the story transform every Jew's sense of the possibility of a divine encounter in the Diaspora [Babylonian Exile]....In fashioning their allegorical narrative, the authors of the Book of Exodus mythologized an array of rituals that were likely part of ancient Near Eastern society for centuries."
--The New Union Haggadah, "The Biblical Exodus," Rabbi David H. Aaron, PhD., Hebrew Union College--Jewish Institute of Religion, Cincinnati, Ohio; Italics added.
It is accurate to say that the memories of any connection to a historical exodus from Egypt among the Hebrews connects its dating to this spring festival. So the elements of it were only changed to give it the added significance it grew to have not just from leaving Egypt but longing to go home while in Babylon. Especially in the Diaspora this played an important part in helping to preserving our Jewish culture while living without king, without a temple, and outside our own nation.
But the way this also applies is that whether it was the original Near Eastern spring festival or the Passover that was adapted from such, it was a celebration of a culture, among all its members. As the above haggadah mentioned, actively participating as a partaker in the Passover meal is meant to "transform every Jew's sense of the possibility of a divine encounter" wherever they may be. No participation, no "divine encounter."
Thus the Jehovah's Witness way of observing the Memorial cuts off a majority from that underlying "divine encounter" designed into the original Passover meal (and likely into Jesus of Nazareth's own reason for employing its emblems the way he did). When you tell others they are not to partake, it's really a way of saying, "You don't deserve to encounter the divine" or worse, "You are incapable of it and not even chosen for this divine encounter."
It has been transformed from a festival of inclusiveness that unites and preserves a society to a ritual of exclusion, reminding people of what they are not, not of what they are as the Passover does.
