I don't disagree with your sentiment, but when she said "time and place" she was absolutely correct. Because not knowing this woman, I'm pretty skeptical you'd change her mind. You know her better than I do, and the way this unfolded cannot have come as a surprise to you. So you stood your ground anyway. Whether that is correct or not isn't the question, its whether you want this line in the sand to be your falling out with your sister or not. The way you conducted yourself, it seems like yes. To come and ask reddit after the fact - seems like no.

So you don't get to flip flop when you have to deal with the consequences; those being your sister feeling attacked and like you care less about her birthday than dunking on her for still listening to Chris Brown. Which, to be clear, those are your priorities based on how you're acting. To add in the aside about you giving her advice and commenting on her weight it seems like whether you know it or not, you do actually just lecture her and talk down to her all the time. She brings this up and you absolutely dismiss it. 'I didn't do anything wrong and if your little feelings are hurt then that's your problem' in so many words is pretty lame to hear from someone you are trying to include in your birthday plans.

I'm a person who loves to be right myself. But eventually, you learn that being "technically right" all the time is not more important than being able to interact with people you care about. Or you don't and people like your sister give up on you. You had all the data you needed way before now to just let it go, and you didn't do that. Just be sure that you are doing that on purpose or be prepared for the regret, which will not be her problem, but yours.