The prohibition of mixing two fabrics only applies to mixing Wool and Linen together.
Cuz....the priests wore linen and wool in their vestments. Don’t impersonate a priest. That is the priest only uniform.
A modern day analogy might be.. don’t wear a blue uniform and a heavy small heraldic badge and a holster...unless you are a duly appointed police officer. Or go into a courtroom with a long black robe in the USA unless you be the official judge.
So many of the laws were written to cover conditions the modern world knows nothing about.