Our Gemara on Amud Aleph discusses the halacha that shaatnez, a forbidden combination of wool and linen, is permitted in the priestly vestments.

Why does the Torah make this exception? It is also interesting to note that the Torah allows shaatnez by tzitzis, so that the techeles sky-blue thread can be wool and the other threads linen (Yevamos 4a). By studying the exceptions to the rule, this also allows us, inductively, to reason and understand the rule itself. Another distinction of this linen and wool combination is that it appears in many of the materials used to manufacture the curtains and covers of the Mishkan (see Shemos ch. 26). What common thread binds all of these rules and practices?

In general, what do the Rishonim state about the prohibition of shaatnez? The Rambam (Moreh Nevuchim III:36) explains that the idolatrous priests would use this combination of animal and vegetation (wool = sheep and linen = flax) to summon magical and demonic powers. The Ramban (Vayikra 19:19) also keys into the mixture, but does not see it as idolatrous, rather as representative of not respecting the natural boundaries and categories created by God. It is an extension of the prohibition of crossbreeding animals or produce, and perhaps a warning in modern times against genetic engineering.

Zohar (III:86b) ties this mixing into the saga of Kayin and Hevel. Kayin, unfortunately, was a product of the “other side,” the serpent. His sacrifice was from vegetation—an earthy, non-spiritual base place. While Hevel was a product of Adam and Chavah’s spiritual side, his sacrifice was from the flock, the wandering, non-physical spiritual component of existence. The Zohar (ibid) states that shaatnez is permitted by tzitzis because there is a wholeness in the mitzvah that allows the proper integration of the two sides, physical and spiritual. This hints at a broader idea of a future messianic perfection and elevation of the physical world so that it can join properly with the spiritual. Rabbenu Bechaye (Vayikra ibid) extends this idea to the Beis HaMikdash and Mishkan, that at least in that area there is already a harmonization of these two powers, allowing the mixture in the materials and priestly vestments.

But that state is not only reserved for the Temple or the messianic future. We also have a daily opportunity to wear our own priestly garments as a priestly people (Shemos 19:6) by wearing tzitzis. At the moment of fulfilling that mitzvah properly, we channel this state as well, where the spiritual and physical are in harmony.

(This is based on an extensive essay and ideas brought forth by Rav Yitzchok Levi, Etzion.org.)