Okay, this is one of Sanji's bad quote when it comes to general ideal towards women in real life but since OP is fictional story, this can applies well.
I don't want to defend Sanji's behavior or anything like that but his chivalry is what makes him respect woman because the only woman that treated Sanji nicely in his childhood is his mom and Reiju.
About Sanji's quote, he's not entirely wrong.
Sanji formed his own team to rescue Robin. And Sanji saw through Robin's lies about wanting to leave the crew.
Robin told Sanji to get out of her business because she doesn't want the Strawhats to get involved in her mess. Just like how Sanji told Luffy and Nami to leave him so that they won't get in conflict with Big Mom in WCI.
Usopp told Robin to have faith in Luffy.
Just like how Sanji have faith in Robin to take care of things Sanji can't do.
Sanji's chivalry has been build since then.
Sanji have too much pride which is one of the reason why people tend to dislike Sanji's character. That's why he have to throw away his pride and wear the RS despite the fact that he doesn't need any support from his family. Nami even told Sanji to give up his pride because if he gets killed then it would just be pointless overall. But he's been like that since childhood. Which is why Nami replaces Sanji to defeat Kalifa just like how Robin replaces him to take care of Black Maria. It's called bonding trust. Most people saying some dumb shits like "Oh Sanji snitched on Robin and reveal her location."
Like, n1gga, we're on a war here. There's no way Robin wouldn't get exposed her identity here. Conflict is bound to happen. And even Robin was happy to have Sanji called for her. And Sanji asking for help is not a bad thing. Nami and Robin both also asked for help.
Move on to Viola.
Viola tricked him because she's an enemy. But Sanji saw through her lies and say that Viola have a beautiful heart which applies to some of the panels above ^^
Because of that, Viola summit to Sanji and claim back her initial thoughts about Sanji.
Move on to Pudding.
Again, despite Pudding being an enemy, Sanji doesn't hesitate to save her even though Pudding broke his heart.
And guess how it turns out?
Sanji's chivalry and charisma sometimes is bad but most of the time, it's worth it.