The Support Conversation was about how the character in question, Soleil, was having trouble fighting on the battlefield because she kept getting distracted and flustered by cute girls(as quoted by her, she felt like she could faint), so she, herself, asked for help from the Main Lord, Corrin, in trying to avoid getting distracted and flustered.
Corrin tries to help her by, more so controversial, slipping a magic powder into her drink without her consent that makes her see all the men in the army as women, including Corrin himself(which isn't hard to imagine when you have Female Corrin), and he's tries to help her with this by trying to play a damsel in distress in need of Soleil's aid to overcome her distraction and flustering. She has issues at the beginning, but she starts to get better to the point where she wants to see what the other men look like as women and even attempts to go and flirt with her dad's boss(Xander->Xandra).
Regardless, on the A-support, Soleil hasn't quite gotten over it, but she has gotten better at not getting distracted and flustered by girls on the battlefield and thanks Corrin for helping her for how much she's gotten better with it. Then comes the S-Support with confessions and whatnot, but when it comes to Soleil's reasoning for loving Corrin, it's because she fell in love with Corrin's Female self and not so much Corrin himself, which annoys him, but nevertheless accepts it.
So no, the original was Never about Gay conversion and Soleil was never "converted". Corrin was never trying to convert her, but trying to help her not to get flustered and distracted by cute girls on the field of battle after she had asked for his help. If anything, the more controversial part of it is the "powder", as while Corrin's intention was good, not asking for consent was not.
Regardless, in the US version, the whole deal was changed to a hypnosis/blindfolded scenario, where after getting Soleil's consent, Corrin blindfolds her and has her imagine him as a damsel in distress(which then leads to Soleil imagining herself flirting with "Xandra". As for the S-support, Soleil does fall in love with Corrin, but even admits that she wants to take things slow.