I outed myself to my supervisor at my previous internship place. I just felt like I needed to give a better explanation for my social awkwardness than just "it's just how I am, I can't help it" etc (it was customer service job so being social was mandatory).
I have also told about my transition to the people who work with me at the local job center for pretty much same reasons as stated above. I'm aiming to work in customer service and overcome my social awkwardness but it may take some time, given my background and tendency to overthink social situations.
In both cases, nothing really changed. The supervisor actually thanked me for trusting her enough to tell such a thing and the people at the job center asked few questions about the process in general (considering one of them was a social worker so it's probably a great chance for her to learn something as well).