I dont tailor anything to my pets based on gender but for kids I think its almost impossible to avoid. They're so different and they regularly express those differences. If I tried to treat a little girl and little boy with equal feedback they'd get bored. I'm a man and I can feel the gender differences, when im hanging out with the kids in my family I enjoy the games we play with the boys and not gonna lie I do not enjoy the games we play with the girls i find them boring. But even then there is plenty of overlap where both are treated the same and enjoy it.
As for pets the only role gender plays for me is the expectation of behavior. I dont think about it 99% of the time.