I used to let delivery men use my bathroom, no problem. Then about 2 and a half years ago I had two men from a family firm come round to deliver a new dining table and chairs. They weren't from a company, they were just deliverers.
The older chap asked if he could use the bathroom before they left (there is one bathroom in my house, which is upstairs) - absolutely fine. I pointed him in the right direction and carried on going over and signing the paperwork / clearing the plastic wrap rubbish, as you do. The younger chap was downstairs with me. I heard shuffling about upstairs and went to take a look, which seemed to make younger chap nervous. Caught older guy coming out of bedroom door "Oh sorry, sorry, couldn't find it."
The bathroom is on the landing and quite obvious.
At this point was feeling very uneasy (I was on my own) and got them out as quickly as I could. After they'd left I gave everything in my room the once over and all seemed OK.
Three days later my house was burgled. Nothing was trashed - it was a neat job. The burglars had gone right for the drawers in my bedroom where all my jewellery was kept. They didn't need to turn anything upside down as they knew where to look. The heirlooms from my grandparents, 21st birthday presents from my parents, an old, broken but valuable, pocket watch my great grandfather had in WW1 was gone. It was all gone 
I was lucky in that some was recovered (I thank god I got my mothers engagement ring back) but most was never found.
The people who carried out the burglary were friends of the delivery guys. They had a routine. It turned out they'd done this before - I was the third victim.
So no, I will never let anyone I don't know come into my house and use my bathroom. It took me months to feel safe in my own home. I'm aware that most are fine but I'm not willing to take that risk ever again.
I don't care if you think that makes me precious or mean or paranoid. I hope you never have to experience feeling your home and your safety has been violated totally and completely. I hope you never have your confidence and your trust destroyed so utterly. If you still think that a strangers need to use a bathroom trumps my right to feel safe in my home, then Fuck You, quite frankly.