What Was the Purpose of the Command against Mixed Threads?

Adam Parker of Bring the Books has an
interesting take on why the Israelites were commanded not to use mixed
threads in their clothing:

This view says that the passage is not prohibiting mixed threads because it was
the clothing of prostitutes. Nor is this prohibition merely meant to be a
picture of holiness and Israel's distinction from among the nations. Rather,
this prohibition had a very practical purpose. Numbers 16:1-40
records an incident when the laity sought to take priestly duties for
themselves. In this view Deut.
22:11 (and Lev. 19:19)
actually address a real and pressing issue: namely the temptation for the laity
to resent or break down the distinction between priests and laity among the
Israelites. Given this understanding of the prohibition of mixed threads,
we see that God is placing barriers between the people and the Levites to keep
such events as the rebellion of Korah from taking place. It is also easy to
explain to the skeptic why Christians no longer observe this prohibition. Since
the New Testament no longer distinguishes elders from the laity by clothing
this command regarding mixed threads is no longer relevant except perhaps in
terms of a persistent recognition that the Church still has leaders and elders
whom the members are to submit to (Hebrews 13:17).

So rather than the command being about a separation between
the Israelites and other nations, Parker says it’s about making a distinction
between the priests and the laity. This sounds reasonable, especially since
there was a similar prohibition
against the laity using the particular blend of incense that was only to be used
in the tabernacle (later, the temple) by the priests:

Then the Lord said to Moses, “Take
for yourself spices, stacte and onycha and galbanum, spices with pure
frankincense; there shall be an equal part of each. With it you shall make
incense, a perfume, the work of a perfumer, salted, pure, and holy. You
shall beat some of it very fine, and put part of it before the testimony in the
tent of meeting where I will meet with you; it shall be most holy to you. The
incense which you shall make, you shall not make in the same proportions for
yourselves; it shall be holy to you for the Lord. Whoever shall make any
like it, to use as perfume, shall be cut off from his people” (Exodus
30:34-38).

But I don’t think this prohibition against mixed fibers for
the laity need be merely a practical command meant to maintain the proper,
ordained authority structure (and I think Parker might agree with me on this). When
creating the Israelite culture through the Law, God used many visual parables
to illustrate the setting apart of the holy from the profane. Those who were
ordained to stand before God for the sake of the people were set apart in a special
way because God is holy, great, and
beautiful. All the commands for the specific clothing, the decorations, and
the objects in the tabernacle were meant to express this truth about God.

You shall make holy garments
for Aaron your brother [the priest], for
glory and for beauty (Exodus 28:2).

You shall also consecrate [the items in the tabernacle], that they may be most holy; whatever touches them shall be holy (Exodus 30:29).

[Those not ordained to do so] shall
not go in to see the holy objects
even for a moment, or they will die (Numbers 4:20).

The separation between man and a holy God wasn’t just
explained to the Israelites, it was experienced and seen as they lived out the
commands of the Law every day. God spent more than a thousand years preparing us
for Christ in this way. Try to read Hebrews
7-10 with the eyes of those who lived the holiness code in the Law—those
who were always at a distance from God because of their sin, those who were
required to participate in the endless cleansing rituals reminding them of this
distance—and you will be awestruck at what it means to be united to Christ, our
priest, who has truly and finally made us holy, tearing down the curtain
separating us from the most holy place where God dwells.

And Jesus cried out again with a
loud voice, and yielded up His spirit. And behold, the veil of the temple was
torn in two from top to bottom; and the earth shook and the rocks were split
(Matthew 27:50-51).

Parker goes on to explain why he finds this view of the
mixed fiber commandment compelling:

a) It has ancient pedigree….
b) It accounts for the previous command for the priests to wear mixed
threads….
c) It allows for harmonization within the Pentateuch rather than
disharmony.

You can read
his full post here.