My concern with allowing transgender people to use a bathroom that doesn't match their biology is that it will make it easier for a pedophile to take advantage of this to hurt a child. I'm not accusing transgender people of being pedophiles. I'm saying pedophiles will use any opportunity to do evil. This is why we've seen them in churches as priests and ministers. This is why we find them in our schools as teachers. Less than 1% of the population is transgender, but 24% of our population is under 18. I'm just more concerned about protecting the safety of children, than making an adult feel better about themselves.
I feel public bathrooms run by the government or schools should only allow people to use the bathroom that matches their biological gender. If someone gets gender reassignment surgery, then they should be allowed to use the bathroom that matches their new gender. But just because you feel you are a different gender doesn't make you that gender. We should look into offering more unisex/family/private bathrooms that only allow single use.
As for private businesses like Target they should be allowed to do whatever they want, but if something terrible does happen they will be open to lawsuits. As a customer I have the choice to decided if I want to go to that business or not.
Fact is 1% of the population doesn't have the right to change all of society social norms.