Your ex is your child's father and gets to decide what's appropriate and not appropriate when she's in his care. On his parenting time, your opinion isn't relevant and you have no control.
Just like when your daughter is with you, you decide who its ok for her to be around and what's appropriate.
Personally, I'd simply focus on other things rather than obsessing over your ex's personal life. Your daughter will be fine and will determine for herself what things she thinks are ok and not ok.
Enjoy your free time and relax. Accept that you cannot control everything and let her dad manage how he parents his child on his time with her.
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