We read in Parashat Vayigash of Yaakov's descent from Canaan to Egypt, where he settled to escape the famine that devastated the region. The Torah tells (beginning of chapter 46) that Yaakov stopped along his journey in the city of Be'er Sheva. According to the Midrash (Bereishit Rabba 94:4), in Be'er Sheva Yaakov cut wood from the sycamore trees that his grandfather, Avraham, had planted in that city many years earlier. Yaakov brought this wood with him to Egypt in anticipation of his descendants' construction of the Mishkan from sycamore wood after their departure from Egypt.
Rav Yaakov Kaminetzky, in Emet Le-Yaakov, explains that Yaakov found it necessary to take this wood with him to serve as a constant reminder to his descendants of their heritage and roots. God appears to Yaakov in Be'er Sheva and declares, "Do not be afraid to go down to Egypt, for I will make you a great nation there" (46:3), implying that Yaakov had been concerned. Seforno explains that Yaakov feared his descendants' assimilation among the Egyptians and gradual disinterest in their origins. The sycamore wood from Be'er Sheva served as a tangible vestige of Benei Yisrael's roots, and of their future destiny to return to Eretz Yisrael. Yaakov therefore made it a priority to bring this wood with him as he brought his family to Egypt.
Rav Yaakov returns to this Midrash in his comments to Parashat Vayakhel, in the context of the verse, "And anyone who had with him blue dye and purple…brought [them for the construction of the Mishkan]" (Shemot 35:23). As Rashi comments in Parashat Teruma (25:4), the terms tekhelet (blue dye) and argaman (purple) refer not merely to the colored dyes, but to wool dyed in these colors. Accordingly, it emerges from this verse that anyone who happened to have with him wool dyed in the appropriate colors donated it for the Mishkan. Accordingly, Rav Yaakov infers from this verse that the wool used for the various accessories in the Mishkan, including the garments of the kohanim, did not have to be dyed li-shma – with the specific intent for the mitzva. The Torah tells that anyone who "had with him" dyed wool could donate it to the Mishkan, even though it was obviously not dyed with this mitzva in mind. The bigdei kehuna(priestly garments) would then differ from tzitzit, in that the tekhelet strings of the tzitzit – at least according to the Rambam (Hilkhot Tzitzit 2:33) – had to be dyed specifically for the purpose of the mitzva.
But Rav Yaakov then dismisses this proof, in light of the aforementioned Midrash. That Yaakov brought wood for the Mishkan with him to Egypt, and this wood was preserved for 210 years and used in the construction of the Mishkan (see Rashi, Shemot 25:5), might indicate that at least some members of Benei Yisrael were cognizant of and concerned about the needs of the Mishkan throughout this period. One might therefore contend that some among Benei Yisrael prepared other materials, as well, in anticipation of the Mishkan's construction. If so, then the dyed wools donated for the Mishkan may have indeed been dyed with the Mishkan andbigdei kehuna in mind, thus meeting the criterion of li-shma. Accordingly, Rav Yaakov concludes, this verse provides no proof that the dyeing process did not require li-shma.