You wash underwear in the washer, work clothing, socks etc do you worry about those things transferring germs to the washer? Of course not. You use washing detergent every time don’t you, that’s what detergent does same as when using a detergent to wash dishes. If you keep your washer properly maintained with no standing water left in it, run a clean cycle as recommended then there is absolutely reason you not to wash your mat as long as the instructions on the mat itself say you can machine wash it.