Was Rabbi Yossei a member of Beth Shammai?
I am talking about the Rabbi Yossei of Berakhot Perek 2 Mishna 3. He is opposed in this Mishna to Rabbi Yehuda, a member of Beth Hillel.
According to Tosafos Yeshanim at the end of Maseches Yoma, stam Rabi Yosei is Rabi Yosei ben Chalafta. So I'll point out these ideas from here http://www.jewishencyclopedia.com/articles/8789-jose-ben-halafta Which point to him being non-affiliated with either school.
It is very likely that he studied much under his father, Ḥalafta, whose authority he invokes in several instances (B. Ḳ. 70a; Me'i. 17b). But his principal teacher was Akiba, whose system he followed in his interpretation of the Law (Pes. 18a; Yeb. 62b).
He was opposed to controversy, declaring that the antagonism between the schools of Shammai and Hillel made it seem as if there were two Torahs (Sanh. 88b). For the most part, Jose adopted a compromise between two contending halakists (comp. Ter. x. 3; 'Er. viii. 5 [= 86a]; Yoma iv. 3 [= 43b]).