I think more folks need to understand that "hey I didn't like that joke" or "hey I know you didn't mean it that way but that hurt me" as inherently being shamed by someone, or even shameful at all. People are messy! We're going to step on each other's toes even when we're doing our best. I think OP did an absolutely perfect job of saying, oh, you're correct, that wasn't my intention, let me make sure that's clear to everyone right away. And then no one has to make any fuss about it from there. At the end of the day, your feelings about being gently corrected are yours to deal with, not the responsibility of the person or people correcting you.

And to be clear, I know this is difficult! It's emotional labor you have to do. If you want to reframe your feeling of shame as something else (I like gratitude personally, like my friend has told me I have something in my teeth and I should fix that before I talk more), that can be useful.

Ultimately, trans people and other minorities don't owe you gentleness when they're hurt. It helps to be nice and low expectations like I have tried to be here, but that is a privileged position. It isn't easy to hear someone lash out at you in pain and say "thank you for sharing this with me, I will reflect on it" but I'm telling you, it is worth it. Listening to other people is so important to protect minorities in any majority-ruled democracy.

And like I said, no one has to do this. But this is the process by which you can take casual allies of circumstance and make them trusted friends. And I think we all need more trusted friends nowadays.