Ultimately I think your reasoning is the correct one. People should be allowed to do what they like if it’s not hurting anyone else or hurting society (how much latitude they should have to hurt themselves is a bit more arguable). Whether someone is ‘born this way’ is an empirical question, not a moral one.
To take two opposing examples: there’s good evidence that sexual attraction to children is inborn, but that doesn’t mean it’s okay to act on it. It does inform how therapists try to treat people who experience it. And on the other side, being a furry is probably strongly influenced by growing up watching animal cartoons, but it doesn’t harm anyone, so it’s not okay to be hostile and shun them.
Yet the ‘born this way’ argument is presumably an effective one, or it wouldn’t be pushed so strongly. Most people know about the evidence that sexual orientation and gender identity are innate because campaigners have brought it to public attention, and we have become comfortable with the idea, whereas research on other characteristics is far less well known and understood. I strongly suspect this is the real reason for @Kimstu’s contradictory beliefs.