Of course it was not right for the Transgender woman to be chased and attacked in Charlotte park, because no person deserves to be the victim of violence. It does not matter what the person's gender or orientation is, every person deserves to live safely in the world. This person had a right to go home safely at the end of the day.
There is no way that anyone can justify the fact that a transgender woman was chased and attacked with a hatchet in Charlotte park. A basic right of all people is to be safe and free from physical harm. To attack anyone without reason or provocation is offensive to all humans.
There's no excuse for physical violence against people at any time. The woman who was attacked in Charlotte park is no exception, regardless of how she dresses or identifies. I hope that the people who perpetrated the attack are brought to justice and are shown as an example of the punishment for intolerance.
No sane person would argue that chasing someone and attacking them with a hatchet is the right thing to do. The person responsible for that should go to prison and/or a mental hospital. I would guess that they have some psychological issues that they need help with. Either way, they need to be somewhere where they will not endanger the public.