No sandals?

Don't know about the sandals and I'd like to get an answer on that. Seems strange. In terms of knees/legs. I like to wear dresses and skirts a lot. It is super easy to keep a pair of leggings tightly rolled in a day bag. Works for cathedrals and for warmth when needed.

FWIW, the Italian version also says no sandals "sandali " (as opposed to just flip-flops).

I've never heard of a rule against sandals...for example, the Vatican has a strict dress code and doesn't care about sandals, or skirts/capri pants below the knee. But that's what it says for this cathedral, so I'd be prepared for it to be enforced. My GUESS is that people in appropriate attire with normal sandals (not flip flops) would be allowed - lots of nuns and priests wear sandals, I've seen them all over Italy in leather walking sandals - but there's no way to be sure. So err on the side of caution, just in case. I think socks with your sandals would be fine, or even a pair of those fold up ballet flat shoes.

Perhaps you can contact them for clarification? Though the Italian site specifies no bare legs or shoulders on the page you linked to, the page about "organizing your visit" lists shorts and bare shoulders as being forbidden (along with the sandals, hats and sunglasses)--no mention of bare legs. So perhaps it really is only flip-flops that are seen as too casual.

While assuming can get you in trouble, I think you are encountering an issue in translation, not literal, but in concept. By "Bare Legs" they likely are meaning no shorts, short skirts, basically above the knee. Same with no bare shoulders, they really mean no shoulderless dresses, tank tops and the like, exposing the skin of your shoulder near your neck would be OK.

I'm just back from Florence, and everyone was wearing sandals everywhere.
It's too hot just now to wear socks and shoes!
I think by bare legs, they mean that you should have your upper legs and knees covered.
At St. Peters in Rome, there were a few very annoyed looking women at the entrance, after being refused admission for having bare shoulders.
They told me to put on my scarf around my shoulders.
It was so hot that day that I had forgotten; though I carried it with me.

Hmmmm.......didn't Jesus wear sandals?

Hmm, I had bare legs below the knee in June. I didn't wear sandals, so I don't know about that restriction.

I agree it must be a translation issue. We just returned from two weeks in Italy including visits to churches in Venice, Florence and Rome. Many women wore sandals. As long as your knees and shoulders are covered, you should be good to go.