I grew up with my mother & my step father. My mother never wanted me to lock any bathroom doors because I got trapped in one when I was like 4 years old (the knob fell off). So I went to the toilet or took showers without ever locking anything up.

A few times it happened that my dad accidentally opened the door while I was sitting on the toilet. He apologized & quickly shut the door again. Stuff like that happens, it's not a big deal.

Just wear some boxers from now on before you go downstairs to be on the safe side. Maybe your GF has some childhood trauma & somehow it triggered her knowing that her daughter saw your naked by accident. Maybe she's just overreacting, who knows. But you guys shouldn't break up because of something that's easily fixed.