Is 'The Taming Of The shrew' a Sexist Play?

The 'Taming of the Shrew' is set in 16th century Padua, Italy. For this play Shakespeare creates a play in a play concerning a wealthy characters, Bapista Minola, need to get his two daughters katherina and Bianca, married. It is a romantic comedy about the battle of the sexes whereas katherina, a well-spirited or 'shrewish' character, is trying to be tamed by Pertruchio, a young, greedy man from Rome, whose mind is clouded by wealth. …

…would not be seen as sexist in the modern world. Yet on the other hand it is sexist I think so because the audience who will have witnessed the play would maybe encouraged to adopt a sexist attitude. Shakespeare maybe has written the play with an element of fun yet having some elements of sexism, which would be acceptable in different centuries. The play it self is not sexist yet the characters in them are.