I am so glad that you came here and are hearing so many words of support!
Daniel's spot-on: they told you they love you
. That's real. And they managed to say it during a time of crisis for them, which is huge. Focus on that part of the conversation.
They have some concerns and woes. They're thinking about sins. Tell ya what: being
is never a sin, a wrong thing, a mistake, or a choice. You just are, and that's good. Someday I hope your family will understand that. They really might someday.
You are a lovely daughter. You shared yourself with your parents in a very real and vulnerable way. Your sharing expressed your love for them and your willingness to let them know you more fully than before. That's wonderful. They have a very devoted and special daughter, who also knows how to balance their expectations and wishes with her own authentic experience and to live her own life while still maintaining closeness with them. I hope they will soon come to see how special that is.
You're probably exhausted today. But I hope you are proud of how you expressed yourself. You did great.