How will we reconcile this Pasuk, which implies that the Avneit of the Kohen Gadol and that of the Kohanim Hedyotos were identical, with 28:40, which implies that all the Begadim of the Kohen Hedyot were made exclusively of linen?
Ramban: This seeming discrepancy is the source of the Machlokes Tana'im in Yoma, 12a, as to whether the two belts were identical or not. 1
Rashi (Yuma 6a) writes that one opinion holds that a Kohen Hedyot's Avnet is pure linen. How can he explain Erchin 3b, which says that Kil'ayim is permitted to [all] Kohanim? Also, the previous verse mentioned Migba'as (of a Kohen Hedyot), and here it says that there was wool in the belt!
Moshav Zekenim: Kil'ayim is permitted to some Kohanim, i.e. a Kohen Gadol. This verse discusses only a Kohen Gadol.
Moshav Zekenim citing R Aharon: All agree that a Kohen Hedyot's belt has wool. They argue about whether or not a Kohen Hedyot may serve with the belt of the Bigdei Lavan (linen) that a Kohen Gadol wore on Yom Kipur. 1
Moshav Zekenim: According to this, we must switch the text of other Gemaros. This is difficult.