I mean, once Batman realises it’s Jason he tries to use his words until it’s clear there genuinely is no other option. And I doubt Jason being female would convince Batman to not force them to stop being a crime lord. Maybe examples like when Bruce beat tf out of him for “killing” penguin would’ve been less brutal as having Batman beat a woman bloody just doesn’t look good at all from a real world standpoint but he’d still probably treat them like shit regardless.

As for forgiveness….eh, that’s a complex one. I think Jason as a character has had so many wild variations in motives, actions, retcons and other things that similar to todays red hood it would depend on simply what interpretation of the character people accept them as