Requirements of covered knees and shoulders in churches/basilicas

Usually yes, at least in the important Italian churches.
The best thing is to bring a light sarong to cover your legs and a light scarf to cover your shoulders. Something very light and fast that you can keep in your purse.

Thank you @ricky!!

Cover your shoulders and knees-both men and women-in all churches (including Pantheon which is a church)

It’s a matter of respect. And also required for admission to most chuches.

You can just take a big gauzy shawl or two. Wrap one around your waist so it falls to your knees, wrap one around your shoulders. Also, I've seen where they either give or sell pieces of tulle fabric for that purpose at St. Peter's Basilica (I didn't need it, so didn't inquire too closely) and I'm not sure whether they do that at other churches as well.

The requirement is only for religious sites -- churches, etc. No requirements for museums, etc. And applies equally to both male and female.

You can buy inexpensive lightweight scarves at every street market you pass if you don’t bring them with you.
I saw 3 girls refused entry to St. Peter’s in Rome for wearing very bare shouldered mini length sundresses ……after they had stood for a long time in the line-up.
They were not happy.

It may be counterintuitive, but having your limbs covered in heat and direct sunlight can be cooler than when all is exposed. I would opt for lightweight, breathable fabrics in lighter colors and / or with a high UPF rating and moisture wicking properties. VFR is a fantastico tour, have a great trip!

A member of my VFR tour had a penchant for wearing tennis super-mini skirts everywhere. We were there in late October, so not exactly shorts weather. The guide repeatedly warned her about the requirements, and there was one church we went to that I could have sworn she was going to be barred from. Somehow either she or the guide conjured up what looked like a poncho to wrap around her legs while we were standing in line, and she was allowed in. She got the message and wore much more modest clothing when we went to the Vatican. Most places we went didn’t have a dress code. You can always ask your guide if there are certain days when you need church appropriate attire.

Wear long loose lightweight pants. No shorts. No mini skirts or skorts. Men should wear a polo shirt or a button down shirt either short or long sleeves. Women should wear tops with any sleeve length. If your top or dress is sleeveless carry a shawl or a cardigan. No flip flops. I recommend good quality well fitting gym shoes to protect your feet on the cobblestones that are everywhere in Europe.

In Florence now, just visited Rome. The stated dress codes for religious sites are as above - cover knees and shoulders, no hats (typically). Also - you may want to verify what is considered religious - for example climbing the Duomo or Campenille in Florence is not religious (but you can’t bring a backpack - you have to check it near the museum - also not religious). It will really depend on the attendants at the entrance. I have yet to see anyone kicked out (except for backpacks where they are not allowed). I have seen shoulders and knees in churches, (sometimes on the same person), and some hats. I’ve been told knees is more typically enforced for women vs men. I adhere to the dress code just in case, and I do bring a scarf/shawl with me to cover knees.

In Spain during hot weather, my wife favors skirts from RipSkirt ( ripskirthawaii.com ) They are wrap type skirts, lightweight, wide range of colors and prints, and the ones that cover the knees certainly are no hotter than shorts, and they look nice. Same with a light top, do you really gain anything by having exposed shoulders?

I favor golf type pants, lightweight and loose, no hotter than shorts and a lightweight shirt.

Having done this tour during a July heatwave, I totally get your concern! For the Vatican and big churches like St. Mark's in Venice, you really do need to dress modestly.

Most museums and other sites don’t have a dress code, though. My wife and I packed a few lightweight options. She brought a thin scarf for her shoulders, and I had a pair of linen pants that could turn into shorts.

We'd usually start our mornings in modest clothes if we planned to visit churches. If it got too hot or we were done with the churches, we’d just change later.

Locals somehow manage to look stylish and stay cool at the same time—lots of linen and cotton, honestly. I’d say it’s worth picking up a few good pieces that keep you comfortable and still show a bit of respect for the culture.

Sarong, pareo, light scarf in your hand bag or light backpack. Wrap them around your exposed legs and/or shoulders before entering religious sites, then put them back after you exit. It works like magic for women.

For men it is best to wear shorts that are long enough to cover the knees, at least partially (unless you don’t mind wearing a sarong). I doubt a man would walk around town with a tan top (Italian men, even young men don’t walk in the city center with tan tops, as it is considered beach wear or something you wear while jogging and it is not considered appropriate for strolling in the city center), so any short sleeve t-shirt will do.