Just as an aside, the Japanese text doesn't include the "because I'm a girl" thing.
Chapter 1:
>Goldlewis: 日を改めるとするよ お嬢ちゃん
Goldlewis : In another day, little lady.
>Bridget: ウチは…… 男です
Bridget: I'm... A man.
> Bridget : いろいろあって 女の子の恰好してるだけで……
Bridget: The girl appearance is because bunch of things happened.
>Goldlewis: ……そう か
Goldlewis: ... Its that so.
Chapter 1 (Bad ending IIRC?)
>Goldlewis:他にUMAを見かけたら教えてくれ お嬢ちゃん
Goldlewis: Let me know if you see another UMA (ユーマ, Unidentified Mysterious Animal), little lady.
>Bridget: ウチは…… 男です
Bridget: I'm... A man.
>Goldlewis: ……そうか それは失礼したな
Goldlewis: ... Its that so, excuse me.
Chapter 7 Bad Ending:
>Goldlewis: あぁ 元気でな お嬢ちゃん いや お坊ちゃんか?
Goldlewis: Ah, farewell, little lady, no, little boy.
>Bridget: お嬢ちゃん でいいですよ
Bridget: Little lady is fine.
>Bridget: ウチは……女の子ですから!
Bridget: because I am... a girl!
The localizers literally rewrote the "calling me miss is fine" as "...because I'm a girl!" He's not trans, even in the bad ending. There's absolutely nothing in the Japanese version that says trans or even discusses gender identity. It's completely made up out of whole cloth by the localizers.
Edit: The 4chan post was missing a line of text. This still only appears in the bad ending and is contradicted by every other mention of Bridget other than this SPECIFIC SINGLE LINE in a specific non-canon bad ending, including all other mentions of Bridget in Strive itself. The good ending that supersedes this ending doesn't mention gender at all and is instead about Bridget regaining his confidence to live his life how he wants.
Seems like a huge stretch to call him trans over that single line, but what do I know?
For reference, here's a video of the Japanese audio of all 3 difficulties, as well as a bonus video of a fight against Test where Bridget appears to call himself a guy, again. https://www.youtube.com/watch?v=7voFmNtqj8A
Here is a video of all the English language stuff, too, but organized in a different way. https://www.youtube.com/watch?v=9W5ezv_xxOk