The Torah prohibits the wearing of a garment which contains shatnez. Shatnez is a garment which contains both wool and linen.
One is permitted to wear tzitzis even if it contains shatnez because a positive commandment overrides a negative commandment. Wearing tzitzis is a positive commandment (You shall make tzitzis) and the prohibition of wearing shatnez is a negative commandment (And shatnez you shall not wear).
The commentary known as the Ra’avid holds that the permissibility to wear tzizis containing Shatnez only applies to wearing them during the day. However, one may not wear tzitzis containing shatnez at night because at night there is no commandment to wear tzitzis. The Mitzvah to wear tzitzis is only during the day, so at night when there is no positive commandment to override the negative prohibition of wearing shatnez, one can not wear tzitzis.
But this heter does not apply nowadays, since we don’t have techeles, as the Shulchan Aruch states explicitly (9, 2) The Rema takes the prohibition one step further, noting that according to some opinions, you cannot tie linen tzitzis even on a non-wool garment. The reason is that someone might come to use linen tzitzis on a wool garment, mistakenly thinking it is silk (Mishneh Brurah 8).
I wonder whether there are some modern-day techeles proponents out there who hold so shtark by the authenticity of their techeles that they claim this whole se’if does not apply anymore, therefore in theory they could tie linen tzitzis on their woolen tallis.
Of course if they did, according to the Raavad you cited, they would have to take off their tallis katan at nightfall and not wear such a tallis gadol on Leil Yom Kippur.