Everything I read about the major Churches and Vatican Museums in Rome stresses how important it is to have shoulders and knees covered. Is this also required in the Baptistry, Duomo and Santa Croce in Florence?

Yes IME

All Italian churches request that you cover your shoulders and knees.

Everywhere in churches throughout Italy. They actually kick you out of many places otherwise.

You should be prepared for that anywhere in Italy.

Not bad actually: three persons posting the same reply at exactly the same minute!

This is a matter of respect.

And franco is right, you can get the boot from churches (or be barred from entry) for not covering adequately.

Men are often asked to remove their baseball caps.

Why do men need to be asked to remove their baseball caps before entering a church?

Why do men need to be asked to remove their baseball caps before entering a church?>

Yes indeed and women have to cover their heads - i guess this makes God a sexist?

"Why do men need to be asked to remove their baseball caps before entering a church?"

Because baseball caps should be removed anytime one comes indoors.

As for the specifics of those three places in Florence, there is no obvious dress code for the Baptistry. There is often a guard/uniforned staff at the entrance to the Duomo, and they can deny entry to inappropriately dressed.
Santa Croce - rarely anyone at the door to enforce the rules, but the expections are that people conform to them.

While some of these religious sights may not have staff posted at the door to enforce a dress code, most sights will have a sign at the door featuring drawings of the preferred type of dress as well as camera use while inside.

What does baseball have to do with anything?

A peaked hat? Or is it a peeked hat?

"Why do men need to be asked to remove their baseball caps before entering a church?"

Because some are too dumb to do it w/o being asked

"Yes indeed and women have to cover their heads - i guess this makes God a sexist?"

Women have not had to cover their heads since Vatican II which ended in 1965.

I've noticed that most churches now allow men to come in wearing shorts, something a few years ago never happened.

What Ellenem said.

Also men should have the common courtesy to remove their hats in any religious building--except maybe a synagogue. I'm not sure about the synagogue.

And get rid of your chewing gum, for gosh sake!

Not "maybe". Men are not allowed into synagogues without their heads covered.

Women are NOT required to cover their head - and every man shold know you don;t wear a hat indoors - ever, unless specifically requied by your religion. It's simply rude.