Camera Policies... Particularly for the Churches / Museums / Cathedrals?

A camera is a camera, as far as their permissible use inside any site. In general, flash and tripods are not allowed. Some sites do not allow photography. In these cases this will be noted on their website, and there will be signage to that effect at the entrance. Expect any employees within the site to enforce the rules.

As for bringing day bags inside with you - this varies. Some will require backpacks to be checked. If you find yourself in a place where photography is not allowed, but your day bag is allowed, as long as your camera is in the bag, no one will care.

even if I keep it in the day bag with no intention of actually using it in the museums?

It will really depend on the museum. Some museums will make you check a daybag.

In general, carrying a camera is not an issue. The size of your bag may be an issue. Some sights (e.g., Borghese) don’t let you carry any bags. Check the rules for the specific museums/churches you plan to visit. If bags aren’t allowed, there should be a cloakroom where you can safely store the bag while you visit.

Sorry - should have specified regarding the day bag. I've already looked into that and have a bag that meets the requirements for size limits everywhere we're planning to go.

It was just the camera size I was wondering about, as I saw some references to "no professional equipment" at some of the spots. I'm probably overthinking it. :)

No, a camera isn't always just a camera. A big camera can connote "professional" to an employee, just like a tripod or a big flash. Meaning you might need a license since they don't know what your plans for the photos are.

As Rick notes, any sight worth its salt will be selling postcards with a much better photo than you can take (nothing personal). I'd suggest you downsize your gear.

That’s a standard SLR camera, nothing large and won’t be an issue in places that allow photography. It is by no means a professional camera in the sense being referred to. Professional equipment is referring to those large camera people carry on the shoulders. Now, if you plan to make money on the photos you take, then your camera would be considered professional. In both cases, museums and churches would impose a fee for you to take photos.

With your day bag or backpack, depending on where you’re at you may be asked to carry it in front of you rather than wearing it. That’s to prevent inadvertently turning and the bag knocking into something. I’ve gotten into the habit of taking it off my back and just carrying it.

Thanks everyone for the feedback!

For my normal day bag, I will be using a 36cm x 25cm x 11cm crossbody bag that can also double as a sling bag pulled in tight to my chest - when I've looked into it, it looks like this will be fine for anywhere I've checked. But, in case I run into issues as Mignon pointed out, I also have a smaller crossbody as 23cm x 17 cm x 9 cm that I can have on hand for the second lens in case the main bag is deemed too large.

Those museums and churches that allow photography usually don’t allow flash to be used because the flash can damage frescoes, paintings etc.

In addition to disabling flash, in churches, etc. you should turn the focus beep and shutter click (and any other noises it makes) to OFF. Your camera should have a "silent" mode, this is definitely when you want to use that. If you're not in the habit of silencing it, find the function to do that now, before you forget to do it when you're struck by a something you want to shoot.

Nobody's going to give your camera a second thought (except maybe the thieves...having a strap that screams "CANONNNNN!!!!" in big bold type will put a target on your back). Just stay aware of your surroundings and keep your wits about you and you will be fine. Have fun.