I don't know if it's sexist, but I don't like it.
Why if I may ask? I lived in the Southeast for long time before moving to Hawai'i so I got a habit of opening up the doors for ladies, pulling out the chair in restaurants, etc. and I think the ladies appreciate that. It's not very common in the Northeast or on the West coast but in Hawai'i you can see it quite often.
I sort of like some of the old traditions, think they show our kinder sides even if it's for a few seconds at a time.
I think you're a lady? So why don't you like the old tradition of someone kissing your hand when being introduced (just curious).
Also, I was a kid so I don't remember but what did/do they say when introduced that way? Obviously not Cześć, right?