We actually had a couple of people pretending to be part of a Jehovah's Witness-esque group use it as an excuse to case houses around here. They were out past legal solicitation hours (it was just past 9PM, IIRC.)
I called the non-emergency police number and e-mailed the neighborhood association when they tried my house (didn't answer the door for them, I wasn't about to open my door to two strangers in suits at 8:30 at night.) I was just calling to report the illegal solicitation. Then a few days later I got a message from the neighborhood association that two people masquerading as a church group were suspected of breaking-and-entering and theft with the usual 'call this number if you have any info' and a quick rundown of solicitation laws that applied to us.
I don't have many more details than that, so the rest is speculation based on their visit to my place: They would knock on the door for ages (which isn't of the ordinary for these groups, but I think they were doing it to make 100% sure nobody was home) and then 'put a pamphlet on the doorknob' (an excuse to check the door and see if it's unlocked.) Nobody bats an eyelash because pushy, obnoxious church groups are nothing new. We used to joke about it, but suddenly I'm actually pretty glad we have a neighborhood watch, even if all they really did was spread awareness. Pretty much the whole neighborhood now has 'no soliciting' signs.
My uncle did that when he was younger. he lived together with my dad,
and used to talk with them for a bit, so one day they came by with a bible for him, but unfortunately he wasn't home, but my dad was, so he asked them to give the bible, afterwards he immediately ran out and threw it on the lawn, to move it over with the lawnmower.
My dad wouldn't let them in but he was a practicing minister at the time.
He'd answer the door, dressed normally, and say "Excuse me, I'm not fully dressed" then he'd get his white stiff collar (commonly known as a dog collar) and come back with it on. They'd usually freak out and leave