My DN told me to just wipe away the first drop and use the second, unless when having reason to expect something to be on my fingers. Judging from your profile picture, you might have children. If so, that means a lot more foodstuff going through your hands than in my life living alone.
Before I used the Freestyle Libre I tested an average of 11 times a day, not practical to wash your hands every time, although some do.
Being a T1 on insulin, I get hypo's from time to time, and I don't think it would be wise to navigate the stairs while hypo to wash my hands before testing!
But washing hands before testing is perfectly fine, and it definitely reduces the chance of getting an off reading!