Ye shall keep my statutes. Thou shalt not let thy cattle gender with a diverse kind: thou shalt not sow thy field with mingled seed: neither shall a garment mingled of linen and woollen come upon thee. Leviticus 19:19
As we can see, the fringe with the blue thread was not just worn by nobility, it was also representative of priestly dress. Most ancient Israeli garments were made of linen, both because of its easy availability and because linen garments were cooler to wear than wool.
Ancient cultures had a great deal of difficulty dying linen, so scholars assume that all dyed cloth (or threads) are wool. Some feel that the prohibition against sha'atnez–the wearing by ordinary people cloth containing both wool and linen is because such garments would resemble priestly garments that were permitted and in some cases required to be made of both linen and wool.
By mixing a wool tassel on a linen garment, "the ordinary Israelite was...in a small way, wearing a priestly garment." "Weaving a ...[blue] thread into the tsitsit [ fringe on a tallit] enhances its symbolism as a mark of nobility. Further, since all Jews are required to wear it, it is a sign that Jews are a people of nobility. Their sovereign, however, is not mortal: Jews are princes of God."
(Milgrom, Jacob, "Of hems and tassels: Rank, authority and holiness were expressed in antiquity by fringes on garments," BIBLICAL ARCHAEOLOGY REVIEW, v. IX, # 3, May/June 1983, pp. 61-65.)