Sure he was. And why shouldn't he be? Having consensual sex with lots of women is fine. It's the future, they don't need to be bound by the morals of today.
Pregnancy isn't an issue (except when he had amnesia and was understandably not able to take whatever meds he needed to prevent it). STDs don't seem to be an issue. So why not?
Kirk liked women and women liked Kirk. Then they had sex. That's what grown ups do.