1. Question: Why can a kohen wear his priestly garments which has shaatnez in them even when not doing the holy service but the Raavad holds you can’t wear tzitzis which has shaatnez in them at night since there is no obligation at night?
A. These are examples of a positive mitzvah pushing off a negative mitzvah, in this case the mitzvah of tzitzis or priestly garments pushing off the prohibition of shaatnez/forbidden mixtures.
B. Really when it comes to the priestly garments the Torah didn’t just push off the prohibition of shaatnez but completely permitted it because that’s the only way to perform the service in the Beis hamikdash.
C. You don’t have to wear shaatnez by tzitzis but if you have a linen garment and the techeiles/blue string (when worn) was supposed to be wool then the positive mitzvah of tzitzis pushes off the negative mitzvah of shaatnez.
D. Why does the priestly garments permit the prohibition of shaatnez but the tzitzis only push off the prohibition if shaatnez.
Answer: The Kovetz Ha’aros (40 in new edition) answered that the Raavad holds that since there is no other way to wear the priestly garments while doing the Holy service then the prohibition became permitted even after the service was done and before it took place but by tzitzis you can always wear a linen garment with linen tzitzis so you wouldn’t need to mix wool and linen together. The Torah just permitted you to do so if you wish for the sake of the mitzvah so the mitzvah only pushes off the prohibition so when there is no mitzva, like at night then the prohibition won’t allow you to wear the garment.