Gemara: [We continue the story of the demand made of Chanina to stop setting the calendar outside of Eretz Yisrael.] [The emissaries of the rabbis of Eretz Yisrael] said [to Chanina]: They said to us: "Go and tell him in our name [to cease]." If he listens, good; and if not, he shall be excommunicated. And tell our brothers in the Diaspora. If they listen to us, good; if not, let them go up to a mountain. Achiya can build an altar; Chanaya can play a musical instrument, and all can apostatize and say: "We have no part in the G-d of Israel." Immediately, the whole nation broke out in crying and said: "Heaven forbid; we do have a part in the G-d of Israel."

Ein Ayah:It is important to realize that Bnei Yisrael is its own distinct and unique entity in the world, with its own special laws. It is not merely due to the needs of a simple religion within which a person tries to draw close to his Maker in actions and thoughts. If the focus were just on the individual, not the nation, there would not be a need for such a separate nation. It would suffice to inculcate the people with a spirit of Torah and attach an emotion of sanctity, as is common among nations, and we could serve Hashem in a manner that is compatible with the service of other nations.
That is why the emissaries talked about going up to a mountain, which symbolizes that which is common among the nations of the world. The foundation of Israel is from Yaakov, who called his place of worship a house (see Pesachim 88a), which is set off from its surroundings by walls. The separations are not just to provide individuals with their own eternal spiritual experience. Rather, Hashem’s idea is for Israel to be a special nation with a special character. Specifically through this standing of uniqueness, when the nation will maximize its spiritual potential in the End of Days, it will bring great light to the whole world.
For this reason, it would be a bad mistake to join in the service of Hashem with other nations before that point, even if the latter accepted basically correct tenets in certain areas of philosophy. This is a mistake that could occur if someone saw the Torah as a religion of the individual, for his personal enrichment, without stressing the idea of the "Torah of Israel."
The mistaken could go and build an altar outside of Eretz Yisrael, which they would find appropriate when this is what their spirits dictate it. Similarly the desire to play a musical instrument is logical when one does not realize that well beyond individualism lies the foundation of the Torah, which can light up the whole world from the light of Israel (see Yeshaya 10:17). The deep personal gain that individuals receive from their Maker stems from the great gift that Hashem will give the Nation of Israel and the whole world. This occurs when Israel stands as a strong nation with special characteristics, when the people will return to Him specifically in the Land of the Forefathers, which they received as an eternal inheritance.
Thus, the part that everyone has in the G-d of Israel is possible only when they join their individual service of Hashem with that of the nation, thereby connecting it to the holiest, most complete spiritual goals. When one distances himself from this connection, he loses his connection to the G-d of Israel as well. Therefore, one must learn and fulfill Torah with a belief in the nation, which is connected to the covenant with Hashem and His Land.
When the people reconfirmed their connection to the national Torah, they emotionally felt the sanctity of the forefathers and the covenant, which explains their weeping. They stated their true desire to avoid the mistake of individualism and committed themselves to the value of the nation in its Land, bringing light to all nations of the world, proclaiming: "We have a part in the G-d of Israel."