The Mishna in Menachos 4:1 says that the mitzvah of the white tzizit is not gone if there is no techelet, and the mitzvah of the techelet is not gone if there is no white. That seems a straight forward enough statement.
However, the gemorah's reponse to this statement is essentially a "Are you crazy? How could the Mishna say this?" They then comment that "Obviously, they mean if the tzizit are torn or ripped, it doesn't invalidate your tzizit as long as a "tuft" of the blue is remaining, or vice versa. They then go on to ask what the minimum size of tizit must be before they get turned into tufts.
When Techelet no longer became available during the Geonic period, they obviously said it was ok to have tzizit without techelet.
What was their rationale, i.e. how did they ignore the Gemora, or is there another gemora which contradicts the Gemora in Manachot?
Was the idea of hinuch, so we don't forget about tzizit at all, enough of a reason to possibly violate a Torah commandment of purposefully putting on a four corner garment to put on incomplete tzizit?
(see Sefaria for translation of sources that led to this question: Menachos 38a-40a)