So people have different opinions. That's why we need statistical facts to determine if trans people increase any actual problems using their identified gender restrooms.
What statistics reveal the emotional effect of bathroom sharing?
What statistics reveal the emotional effect of sharing lunch counters with black people?
Statistics generally deal with matters where there is some legal record. I.e. actions that cause harm. We know a certain number of sexual assaults by cis men happen in restrooms. What are the numbers on trans women using women's restrooms? And possibly more telling: how do they compare to numbers when trans women are forced to use men's restrooms? Care to wager on where the higher rate of assault happens?