Are modest knee length shorts acceptable around towns and cities in the day time?
You are certainly free to wear what you wish. If you will be visiting churches, best to have a way to cover anything on you body that bends.
As for general acceptability, if you are in a coastal tourist town, anything goes, further inland,more conservative would be better.
Barcelona's Cathedral and Sagrada Familia are two examples of churches with more tourist crowds that may feel the need to enforce a modest dress policy, but enforcement can depend on who's working that day and other factors. A lightweight wrap is a pretty cheap insurance policy.
The Barcelona Cathedral has a sign at the entrance. Your knees, elbows and midriff need to be covered. It's the first time I've ever seen a sign explaining the rule, but not the first time I've encountered dress codes for Cathedrals. Italy and Spain are the places most likely to enforce a dress code.
The dress code is about modesty, not wearing nice clothes. Flip flops are fine, short skirts or spaghetti straps aren't. Shorts would be acceptable only if they cover your knees, capri length is always a safe choice.
Like Laura says, enforcement can be inconsistent. One morning no one seems to care, the next they are strict.
Everything I've read about what to wear has said that most locals don't wear shorts except for in the beach towns but I have also had people on this forum say that wasn't true. Yet most guidebooks and information I find written on the internet (in very reputable places, including Rick Steves!) also state that they don't normally wear shorts. I have seen some churches in Europe enforce rules about making sure shoulders and knees were covered so we always make sure we do at least that on days we plan to visit churches.
most small churches in most of Europe don't have the staff to enforce their dress codes -- which means that tourists should be disrespectful? not getting it. I imagine most tourists could outwrestle a nun if necessary too.
Cover anything on your body that bends?
That would mean gloves long enough to cover all your fingers and your wrist. Ankles would have to be covered with socks unless your pants are long enough, and, of course, no sandals.