Why is shatnez (a garment made of a mixture of wool and linen, which is forbidden) muter (permissible) by tzitzis?
In short: The Torah says in Devarim 22: 11 - 12:
You shall not wear a mixture of wool and linen together. You shall make yourself twisted threads, on the four corners of your garment with which you cover yourself.
We learn from this juxtaposition of pesukim that one can even make Tzitzis in a case of Shaatnez.