(a) On 78a we prove that R. Yosi holds that Tum'ah is not Hutrah b'Tzibur from a Beraisa in which he says that we sprinkle Mei Chatas on the Kohen Gadol on days three and seven of his separation before Yom Kipur.
We must say like Tosfos (Yuma 8A), that the proof is because we sprinkle mi'Safek, but all agree that if he is Tamei we must Metaher him.
I would have thought that a better proof of this is that?? ??l'Chatchilah he must offer the outer Chatas in Taharah to allow Kohanim to eat it at night, so Yisrael will get a proper Kaparah!
(b) In the first Mishnah of Yuma R. Yehudah agrees that we separate the Kohen Gadol for seven days beforehand. Isn't this a clear proof that he holds Tum'ah is not Hutrah? Or is this separation not to prevent him from becoming Tamei and to sprinkle Mei Chatas on him, but rather it is learned from Milu'im, or it is to prevent him from becoming a Bo'el Nidah?
Pesach Feldman, Jerusalem, Israel
(a) I think your question is essentially answered by the Tosfos that I believe you were referring to (DH "Ee Savar"). Tosfos asks that the Gemara's proof that Rebbi Yosi does not hold Tumah Hutrah b'Tzibur because he requires the Kohen Gadol to undergo Hazah mi'Safek seems difficult, as the Kohen Gadol must bring an "Ayil Shel Aharon" which is primarily a private Korban. This would seemingly not be called b'Tzibur! Tosfos answers that the Ayil Shel Aharon would still only require sprinkling if we knew the Kohen Gadol was Tamei beforehand, not if we simply want to make certain because of a Chashash. Tosfos explains that this is because the Ayil Shel Aharon is in fact like a public Korban, as we see it is Docheh Shabbos and Tumah. Tosfos is establishing that making a Kohen Gadol do Hazah mi'Safek would only make sense if there was some kind of serious Torah problem, such as Tumah Dechuyah b'Tzibur. I'm therefore unsure why you would want to say instead that the Hazah must be to enable the Kohanim to eat the outer Chatas, which is only l'Chatchila.
(b) It definitely makes sense to say that the main reason for this separation according to Rebbi Yehudah is the Limud from the Miluim. There are other lofty reasons behind this separation as well (see CHIDUSHEI CHASAM SOFER HASHALEM).
Kol Tuv,
Yaakov Montrose