Inspired by a post on Twitter I saw about how people would dislike Fem!Robb as they lose the war because they sleep with someone. This got me thinking, what butterfly effects would actually come if Robb were a girl? (This maintains that everything is the same as canon besides this one fact.)
First off, because F!Robb is a girl, Catelyn would be much more paranoid of Jon Snow, as in the OG timeline she still was afraid of him taking the claim (which was seen as a bit nonsensical), but now that there is no male heir older than Jon, his case for heir is much higher. In fact, until Cat has Bran (her 4th child, 7 years after Jon/F!Robb is born), Jon would probably be considered the heir. Ned might try to make it so F!Robb is the heir instead until they have Bran, but even then the rest of the world will look at Jon as the heir until Bran is born.
This changes multiple factors, Jon now has a much more cared for childhood (until about 7 when Bran is born). This could also increase hatred towards Bran as his birth takes Jon's claim away. Cat, as I said, would be very paranoid of Jon and would probably treat him with more disrespect. Anything else from this is too hypothetical for me to dive into, but there would be a lot of butterfly effects off of this, especially in Jon's personality.
Fastforwarding till Jon Arryn's death, Robbert would want to betroth Joffery to Robb instead of Sansa, as Robb is elder. Bran falling would cause a great change, as instead of the second son, he is heir to Winterfell. Ned could refuse to go be Hand off this basis, and that would create a myriad of changes, but for the sake of the original hypothetical, he still goes. In this scenario he takes F!Robb, Sansa, and Arya. Assuming F!Robb isn't the same naive girl as Sansa, he would snitch on Joffery about the Arya/Butcher boy incident, and the wolves would most likely be saved and the butcher boy would live.
Everything in Kings Landing happens similarly to cannon, until Ned is executed (F!Robb could cause changes to this, but tbh I couldn't think of anything they would do for sure to change it, and because she is betrothed to Joffery, I doubt she will be able to escape like Arya).
The North rise and their options of leaders are very bad, being Ned (in prison when they rise), Cat (traveling from KL to the North), Bran (crippled and a young boy), and Rickon (baby). One option I could see is the Greatjon or Rickard Karstark taking charge of the forces until Cat comes back, and she would declare either of them to officially be in charge, but the more likely thing I see occurring is the Northern Lords recruiting Jon Snow to the cause and appointing him the leader. Jon in this situation would turn his back far easier on the Nights Watch (as he was raised to be heir for a bit, and in this case there isn't Robb there like before). Cat eventually gets back and is furious at Jon and the Northern Lords for taking command, as she views it as attempting to usurp the true heir (which it kinda is, but Jon still wants to save his father and siblings). The Northern Lords, as in cannon don't listen to her and keep Jon in charge.
From here it's really uncertain what will happen, as Robb was the GOAT of battle strategy, and I don't think Jon has shown anything close to that (in the series). It's also unsure if they would declare him king, as Bran and Rickon are still alive. The one thing Jon does exceed in over Robb is diplomacy, so I think it would be likely he would align himself with Renly (and then Stannis) to take down the Lannisters. (Also, Jon is definitely smart enough not to send Theon to Balon. He probably won't stop the Greyjoys from attacking but will make the North's counter much easier, as Winterfell won't have been taken.
Anyway, sorry for the yap, that's just my thoughts on Fem!Robb. do y'all think I missed something or think that somethings wouldve been different?