As has been stated in answer to other such questions, God made covenants with Noah, Abraham, Israel, etc. The Mosaic Law is a specific covenant between God and the Jewish people. This covenant included many things, including the prohibition of wearing clothing with mixed fibers. This covenant was enacted about 3500 years ago, I think. Isaiah spoke of a new covenant that was enacted when Jesus died and rose again. So, the Mosaic covenant was in effect between God and the Jewish nation for about 1500 years, but it is in effect no more.
Certainly, animal sacrifices are no longer required in the new covenant, because Jesus was offered once for all time.
So, for Jewish people living between 1500 B.C. and about 30 A.D., it was applicable. But not today.
Today, there are still sins to avoid, because all sin is to our destruction. While momentary pleasure may be derived from sin, true fulfillment comes as we live in the presence of God.
So, wear whatever fabrics you want, but seek to know God. That is what the Scriptures call us to today.