I always heard that it is not modest to publicly be courteous to woman (if a Jewish woman needs help you should help her,
but if she does not, just you are holding the door for her or giving her the right of way)
(I thought it was an invention of the knight in the dark ages and not a Jewish custom ( https://en.wikipedia.org/wiki/Chivalry ) )
I guess that if she is an old woman you need to respect her
But @DavidKenner told me that Rabbi Shlomo Zalman Aurbach in his book שו''ת מנחת שלמה the opposite of what I always heard
Is this true? Source?
What other Rabbis hold like that?