Responsa for Rosh Hashanah 68:21

They responded: "How pious are these generations!" (Yevamot 39b:15) "All that Sarah says to you, listen to her voice!" (Genesis 21:12) "Go and say to them, return to your tents and bless your God!" (Deuteronomy 5:27, Nehemiah 9:5) The proof is from Channukah candles and megillah reading. They explained to me that just as in these cases, since the women were involved in the original miracle they are obligated to perform the commandment and recite the blessing, so too with the Lulav, we find that the [entire] Jewish people have only one heart directed to their Father in heaven (Sukkah 45b.9). So too with the Shofar, we are taught that the Holy One said: bring me [verses of] kingship, that I may be your king, and [verses of] remembrance, that the memory of your ancestors come before Me favourably, and all of that, with a Shofar. (Rosh Hashanah 34b.7) Now, women also need to be remembered before Him favourably. Therefore, if they recite the blessings for these commandments, they have permission to do so.^*This is also the opinion of Rabbeinu Tam, quoted in Tosafot on Rosh Hashanah 33a:5

R. Jacob, the cantor of Magdeburg, died and left a son, Hizkiyahu, who was worthy to succeed his father as cantor of Magdeburg, though inferior to him in some qualities. A majority of the membership of the Magdeburg community wanted the son to succeed his father, but a minority of possibly one or more strongly objected to the son. R. Moses b. Hisdai was asked for his opinion in the matter. He advised Hizkiyahu to try any measure in his power to ingratiate himself with the objectors. He asked the leaders of the community to direct their efforts toward effecting a reconciliation with the opposing faction, and expressed his opinion that a single person could not defy the will of the entire community. R. Isaac b. Moses (of Vienna) stated that according to Biblical Law a community could not hire a cantor to whom there was objection even by a single person. R. Meir stated his opinion that a cantor might officiate throughout the year even though not acceptable to a few congregants, but that he was not permitted to officiate on Rosh Hashanah and Yom Kippur or on fast days, if even a single congregant found him objectionable.
SOURCES: L. 109–11; Or Zarua I, 21a.