There are places that will ask you to check your camera, but they're few and far between (the galleries at Palazzo Pitti asked me to check my SLR, but I was allowed to take it to the gardens and use it in the courtyards, for instance). Most places will simply ask that it not be turned on (if cameras are strictly not allowed) or not used with a flash (this includes red auto-focus lights if you can turn them off, because they will attract negative attention). If you have an SLR/DSLR in a camera-specific bag with multiple lenses, this will be more likely to attract notice than a pocket-size film or digicam. The guards are generally fairly vigilant, and there's a good reason for the 'no-flash' rules, so follow them.
Every tourist-attraction church you go to will have a sign outside with pictures of things that aren't allowed. Casual dress is OK, but shoulders and knees should be covered (in less strict churches, long shorts will be OK. Capris will always be fine). The less frequented a church is, the more conservative you should be in what you wear.
I've found, from a women's perspective, that sarongs and pashminas are extremely helpful in these situations. Tying a sarong over shorts creates an instant skirt. Pulling a pashmina over a sleeveless blouse/tank top creates a presentable look. You could mimic this with some convertible pants (the kind that zip-off into shorts) and a short-sleeved button down shirt that are in your bag.
For the day that you go to the Vatican, wear longer pants and tops with sleeves so that you don't get stopped by security and put in
paper clothing (not my idea of a fun way to walk through St. Peter's!).