The Mishna states
I'm curious how you know this particular clause from the Mishnah and not know that what you state is actually subject to a Tannaic dispute.
Is this an absolute majority?
See Horayos 1:5. As a quick summary of the various opinions recorded there:
- R' Meir: 50% of the congregation (even of six Shevatim) or 50% of at least seven Shevatim each (even if it's not a majority of all of Bnei Yisrael); if a Shevet follows its own Beis Din, a Karban is not brought.
- R' Yehudah: 50% of at least seven Shevatim who follow the Sanhedrin, or 50% of a single Shevet who follows its own Beis Din.
- R' Shimon: 50% of at least seven Shevatim; if a Shevet follows its own Beis Din, a Karban is not brought.
So, all things considered, majority is basically what you assume it to be; at least a significant percentage of the Jewish populace. Nevertheless, from the example you bring it's clear that you're either unaware or misunderstanding an important point about this Karban: it doesn't matter how long it's been since they issued the mistaken ruling, so long as they haven't retracted yet. Consider Horayos 1:2:
הוֹרוּ בֵית דִּין, וְיָדְעוּ שֶׁטָּעוּ, וְחָזְרוּ בָהֶן, בֵּין שֶׁהֵבִיאוּ כַפָּרָתָן וּבֵין שֶׁלֹּא הֵבִיאוּ כַפָּרָתָן, וְהָלַךְ וְעָשָׂה עַל פִּיהֶן, רַבִּי שִׁמְעוֹן פּוֹטֵר, וְרַבִּי אֱלִיעֶזֶר אוֹמֵר, סָפֵק.
If Beis Din ruled, realized that they erred, and retracted, whether they had already brought their atonement or not, if an individual went and acted on their word, R' Shimon exempts [from an individual Chatas] and R' Eliezer says it's a doubt.
R' Shimon, who exempts even after they retracted, would certainly say that he's exempt if he sinned before they retracted, regardless of how long it was since they ruled! As the Gemara explains his opinion (3b):
אמר רב יהודה אמר רב מ"ט דר"ש הואיל וברשות ב"ד הוא עושה איכא דאמרי אמר רב יהודה אמר רב אומר היה ר"ש כל הוראה שיצאה ברוב צבור יחיד העושה אותה פטור לפי שלא ניתנה הוראה אלא להבחין בין שוגג למזיד
Rav Yehudah said in the name of Rav: "What is the reason for R' Shimon? Since he acted with the permission of Beis Din." Some say that Rav Yehudah said in the name of Rav: "R' Shimon used to say: Any ruling which is disseminated to the public, an individual who performs it is exempt, because ruling was only given to distinguish between mistaken and intentional acts."
According to either line of logic, this should hold whether the courts reversed or not, regardless of how long it's been.
Before I elaborate on R' Eliezer's opinion, let me quote the end of Mishnah Horayos, 1:1:
זה הכלל התולה בעצמו חייב והתולה בב"ד פטור
This is the general rule: One who hangs [his actions] on himself is liable [to a private Chatas], and one who hangs [his actions] on Beis Din is exempt [from a private Chatas].
With that background, let's see how the Gemara explains R' Eliezer's opinion (3b-4a):
א"ר זירא משל דר"א למה הדבר דומה לאדם שאכל ספק חלב ספק שומן ונודע לו שמביא אשם ולא מבעיא למ"ד צבור מייתי דמפרסמא מלתא אלא אפילו למ"ד ב"ד מביאין דלא מפרסמא מלתא אי הוה שאיל הוו אמרין ליה
R' Zeira said a parable for R' Eliezer. To what can this be compared? To someone who ate something which is doubtfully forbidden fats and doubtfully permitted fats, and later he found out [that it was forbidden] – he brings an Asham. It's not needed according to the one who said that the congregation brings the [communal sin offering], because the matter [i.e. that the court reversed its opinion] is publicized. But even according to the one who said that the courts bring it, where the matter is not publicized, if he had asked they would have told him.
But since the doubt only arises whether he was relying on himself or the courts because they had already reversed, had they not yet reversed, he would surely agree that he's exempt!
This is how the Rambam understands this procedure (Shegagos 12:1):
כָּל דָּבָר שֶׁחַיָּבִין עַל שִׁגְגָתוֹ חַטָּאת קְבוּעָה אִם שָׁגְגוּ בֵּית דִּין הַגָּדוֹל בְּהוֹרָאָה וְהוֹרוּ לְהַתִּירוֹ וְשָׁגְגוּ הָעָם בְּהוֹרָאָתָן וְעָשׂוּ הָעָם וְהֵם סוֹמְכִין עַל הוֹרָאָתָן וְאַחַר כָּךְ נוֹדַע לְבֵית דִּין שֶׁטָּעוּ הֲרֵי בֵּית דִּין חַיָּבִין לְהָבִיא קָרְבַּן חַטָּאת עַל שִׁגְגָתָן בְּהוֹרָאָה
Any matter for which one is obligated a Chatas for doing it by mistake, if the Sanhedrin ruled mistakenly and ruled to permit it, and the people erred through their ruling, and they acted, relying on their ruling, and afterwards the court realized that they erred, the court is obligated to bring a Chatas on their mistaken ruling.
"And afterwards." No mention of how long it was in the interim.
As an aside, I'm not convinced that a communal Karban is even brought in the particular example you provide. If the courts rule that there's no concept forbidding eating Kodshim while impure, there's no Karban brought, as they're uprooting an entire concept, not a specific detail in it (Horayos 1:4). (Depending on how you construe the case, "impurity is permissible for the public" (Sanhedrin 12b et. al.) may be relevant, but not necessarily.) As for anyone sacrificing outside the Temple – who gave them permission to do that? If they did so they'd be liable on their own count, as, again, if the courts ruled that that was permissible, they're uprooting an entire body of law. And for your presumption that "even if everyone is at the Temple, most people should be Tahor" – all you need is one dead body under the roof while everyone is there to make everyone Tamei, or else a well-placed Sheretz right at the doorstep such that everyone steps on it as they enter.