You are accurately stating that for a stranger to eat the Passover lamb, they must be ritually physically circumcised, which makes them a member of the people of Israel.
True.
If a person is not ritually physically circumcised, they are cut off from the people, and not to partake of the lamb.
Also true.
The Mosaic law Passover is in remembrance of what God did when He redeemed the children of Israel, bringing them out of the 'house of bondage' which is Egypt.
Hey, we're three for three!
Since the Mosaic law says not to add to or take away from any commandment, this can not be altered.
Fundamentally, I would agree. We all know that things change somewhat, according to whether or not a sanctioned place of sacrifice exists.
So, Yeshua is called the Passover lamb. And the NT Passover is kept in remembrance of Him and what Jesus did to bring us out of the house of bondage.
I think this deserves some teasing out.
After the destruction of the first Temple, the seder was created in Babylon in order to provide a defined customary way of celebrating the Pesach in the absence of the sacrifices. The result is what we might call "a memorial of the memorial".
Once the Jews returned from captivity, and had a restored place of worship, there was a merger between the ancient sacrifices and the relatively recent seder. This process of blending the two continued until the destruction of the second Temple in 70 CE.
Since the destruction of the second Temple, we have simply gone back to the seder created in Babylonian captivity--the "memorial of the memorial". Since there is no actual sacrifice at this time, circumcision has become a moot point. Anybody who wishes to participate may do so.
Now, the standard rubric for a seder includes having the leader expand upon the basic story and the elements on the table as he sees fit. He may discuss current or recent political situations relevant to slavery and bondage (refuseniks, the holocaust), the four cups (each has a name and a meaning), or any other relevant topic.
In Yeshua's case, he applied the symbolism of the seder to his own life and death. We seriously err if we think he literally was regarded as a Passover sacrifice. But we do remember the death of our founder each year in the seder, "as often as you do this". In essence, we include his own midrash, applying the symbolism of the ancient Pesach to his own life and death. In addition, early Messianics seem to have added the ceremony of the burial and "resurrection" of the afikomen, so that the seder ends on a hopeful note, rather than the sour note of continued expulsion from the Land.
Although we do not actually eat Yeshua the lamb, we symbolically recognize that it was the crucifixion of the body of Jesus, the broken matza.
I find this statement a bit on the over-simplified side. What actually happens is, we celebrate a seder, with its original meaning of slavery, blondage, and redemption. We then take that meaning, and apply it to the otherwise meaningless death of an innocent man, Yeshua. As such, we can apply to him the role of Moses, the Deliverer; the Lamb who died for us; the Matzoh, broken for us; etc. Yeshua even made use of the third cup, already known as the "Cup of Redemption", and likened it to a covenantal sharing, which would inaugurate the Promises of the New/Renewed Covenant described in Yirmeyahu/Jeremiah 31.
If the Mosaic law forbids adding to or taking away from any command, and the NT Passover adds in remembrance of Yeshua, then the NT Passover is the Passover of a different covenant.
This is simply inaccurate, as can be seen by the above. We do not actually perform the Passover ordinance today, as described in the Torah. The whole thing is a modified remembrance of the need to perform that memorial... someday.
Plus, the Passover of the Mosaic law required the ritual physical circumcision, but the Passover of the NT requires a circumcision of the heart. Again, that would be taking away the requirement for the physical circumcision from the Mosaic law.
The issue of circumcision related to being in a clean state, enabling one to participate in the sacrifice on the Temple grounds. It was not about sitting and eating a meal. Of course, that point is now moot, since we have no Temple and no sacrifice.
However, if the position is that Gentiles become a part of/members of Israel, and that the Mosaic law applies as in One Law for all, then Gentiles (male) would need to be ritually physically circumcised or they are cut off from the people of Israel per the law.
There is some truth to this. The question becomes one of defining what constitutes a legitimate conversion process. Tractate Yevamot in the Talmud discusses this at length. At the very least, there must be a period of something more than a year, during which the conversion candidate studies Judaism and learns what an oath of allegience to Israel would mean to his life. During that time, there is no such concept as being "cut off", since the individual remains a Gentile candidate for conversion. But he may participate in communal fellowship and study, as per the Acts 15 council decision.