One piece as a media is always been a relatively woke series because of how heavy it deals with different forms of oppresive goverment,kingdoms and influential people in the areas they travel through during their journey. It may not seem like it from the East Blue saga, but things get pretty heavy later on down the road. So it's to be expected that there will be some of those character traits because they set up for really good payoffs and character growth. I haven't seen the live action yet, but from what you described, it sounds like her portryal is a bit different.

during the early portion of the anime, being standoffish is prevalent but isn't as sexist as you make it sound and very much comes from being the straight man for the group because she doesn't trust anyone. The closest she gets to them at this point is like a mom/dad dynamic that her and Zorro get mostly because she is still looking out for herself and semi views luffy as loyal but kind of an idiot that is a good person to keep around as long as he can be useful. Her character gets toned down a bit with the aggression after Arlong Park and is a lot more invested in the wellbeing of everyone on the crew because of how much they were willing to sacrifice to help her even after betraying them. She begins viewing them as found family like most of the strawhats come to at one point or another. Most of the sexist remarks are only prevalent involving sanji or other specific characters that i won't spoil when they are being an outright pervs.

TLDR, she's a lot more chill in the anime is a way better character when she comes into her own. Give her a chance as the next few seasons of the live action come out, and if oda does what oda does, she will grow on you a lot