I submitted this response in the comments. The status was “This comment is awaiting moderation.” Not surprisingly, it wasn’t approved on their site.
From Rabbi Akiva Dershowitz and the “Beis Horaah” (https://dinonline.org/2018/08/22/the-reason-why-not-wearing-techeles/):
Some people wear “Techeles” Tztitzis.
I understand that we don’t know for sure whether it is THE RIGHT Techeles..
But maybe it is..
So why do we see Gedolei Olam not wearing Techeles Tzitzis..?
Thank you very much!
Without getting into the issue if l’maysa one should or shouldn’t wear techeles, to answer your question why certain gedolei yisroel specifically did not want to wear techeles, here are some of the reasons.
The gemora Babba Metzia 61b says one should not tie “kl ilan” (a dye that looks similar to what techeles should look like) to his tzitzis and say that it is techeles. Since it isn’t clear that this is indeed techeles, as there have been numerous people over time that have made claims that they found techeles, therefore it is still questionable, that it may be kla ilan. See Ohr L’tzion 2-42( 13)
In addition for those who have a tradition of not wearing it, by putting it on it makes an impression that we are better than them. (Ohr L’ztion ibid).
In areas that it is not accepted to wear techeles it appears as lo tisgodidu.(Teshuvos Vhanhgos 1-26).
If one has in mind for the mitzvah, when it indeed isn’t the mitzvah it might be baal tosef. (Teshuvos Vhanhagos ibid). This is true especially if the person putting it on doesn’t know that he should think that it is only for the mitzvah if indeed it is the correct techeles.
Aside from this see Aruch Hashulchan O:CH 9, Kovetz reshuvos 1-2, Orchos Rabeinu 1-pg. 246, Sharei Halacha U’minhag O:CH 12. Halichos H’gra U’minhagav 30
1. “So why do we see Gedolei Olam not wearing Techeles Tzitzis”
See https://bluefringes.com/notable-wearers/ and https://www.techeiles.org/techeiles-video-its-not-all-black-and-white/
2. “The gemora Babba Metzia 61b says one should not tie “kl ilan” (a dye that looks similar to what techeles should look like) to his tzitzis and say that it is techeles.”
This is in context with honesty. Here you know you have the right Techeiles and intentionally are fooling something else. With our Techeiles today there is no fooling. Plus there are numerous Rishonim saying that Chilazon means a snail. See:
a) Tanchum Yerushalmi – https://bluefringes.com/textual_sources/chilazon-tanchum-yerushalmi/
b) R’ Avraham ben HaRambam – https://bluefringes.com/textual_sources/rabbi-avraham-ben-harambam-potzea/
c) Raavya – https://bluefringes.com/textual_sources/raavya-on-purfirin-prasinan/
d) Yad Rama – https://bluefringes.com/textual_sources/yad-ramah-on-chilazon/
e) and others – https://www.techeiles.org/library/library-sources/
That doesn’t even begin to touch on the numerous Acharonim stating the dye source including R’ Samson Rephael Hirsch among others.
3. ” by putting it on it makes an impression that we are better than them. (Ohr L’ztion ibid)”
See https://www.mywesternwall.net/2020/06/14/top-10-common-objections-to-wearing-techeiles-today.html Point 5.
4. “In areas that it is not accepted to wear techeles it appears as lo tisgodidu.(Teshuvos Vhanhgos 1-26).”
See 2020/06/14/top-10-common-objections-to-wearing-techeiles-today.html Point 7.
5. “when it indeed isn’t the mitzvah it might be baal tosef.”
See this from R’ Osher Weiss Shlit”a who ironically isn’t pro-murex Techeiles: https://www.mywesternwall.net/2020/06/14/top-10-common-objections-to-wearing-techeiles-today.html