Lilmod,
The Mishna uses the term ?????? for the men coming before women, it does not use that term for Kohanim coming before Yisroel. Furthermore, the Shulchan Aruch only brings down a Kohen coming before a Yisroel for tzedaka, it doesn’t say anything about for saving a life.
Now, there is a machlokes among the Rishonim whether ?????? means for saving a life or for providing tzedaka. But the Rema clearly paskens that a man comes before a women if they are both drowning. The Yerushalmi on that Mishna says specifically that the wife of a “Chaver” (roughly equivalent to a “ben Torah”) comes before an am ha’aretz ??????.