A quick addition to Blue shirt’s brilliant analysis. One of the reasons for NOT wearing “techeiles’ is the fact that, “mi-deoraisa”, if the zizis are dyed with “techeiles” you can THEN have wool tzitzis on a linen “beged”, technically shaatnez, because of “asssei doche Lo saasei”. However, if today’s “techeiles” is NOT the real one then yoU are “oiver’ (transgress) THE “LAV” of shaatnez.
Hence, the Poskim have refused to use “techeiles” for fear that, if it is an incorrect dye, one would be ‘oiver’ the lav of shaatnez. Obviously, all of the people who use it today use WOOL taleisim, nonetheless to prevent any problems, Poskim have preferred to avoid using techeiles altogether.