Question

Hello Rabbi,
Regarding what the Shulchan Arukh rules in Orach Chayim 263: “If the majority of the congregation accepted the Sabbath upon themselves, the minority are drawn after them against their will” — what is the reasoning here? As far as I’ve seen, the early source for this is in Mordechai, Shabbat, section 297, but even there he does not explain it; he only brings a possible source from the Talmud and says it can be rejected.
Someone suggested that this is because of “do not form separate factions,” but that doesn’t seem likely, because there are not two different halakhic rulings here, and not even two different customs. Maybe the issue is separating from the community? If so, is that relevant when it is not in public? Or is there some other reasoning?
 
Thank you