Approve is the proper word.
I was clear in saying she does not need my approval but as humans we cannot help APPROVE or not of something we see. the human reaction of approval or disapproval is instant and unconscious and something you cannot avoid.
You see an MMA fight you either approve, or do not approve of it. Does not mean MMA or their fans care about your reaction.
If I see people making out in public (PDA) I don't approve of that, generally. It is simply something I do not think appropriate. I am not suggesting that should matter to anyone who is not me. it is my reaction to my personal taste.
Edit : also there is nothing wrong, also in attaching your judgement. The issue is more in how you do it. Do you lecture people? Go up and insert yourself in their business unsolicited? Those may cross the line and are not my style. But if my friend is going to a family beach wearing a Borat like outfit above and he asks me about it I could tell him I don't approve of that and tell him why I don't with my judgement being 'it is inappropriate, in my view, around families and children'. If he is breaking no laws he is free to ignore my opinion and I am fine with that.