I never went door-to-door for religious reasons, but when I was younger I was one of those annoying political canvassers for years so I'll tell you some general stuff that was the same in pretty much every state I went to.
It won't stop an idiot but it might give you some angles to approach it.
First, we were always trained that "no trespassing" meant "no trespassing." We would enter fenced yards to approach the door, but only if they were not marked like that. I believe this is a legal thing as someone on one of my teams did ignore it and was cited (or at least warned, been years now) by the police for doing so after the homeowner complained.
Do some research into the "beware of dog" signs, as I've heard that in some areas they may open you up to further liability if a bite does happen because it can be read as a sign that your dog is aggressive. I don't think this is universally true though, and some form of warning that there is a dog in the yard may deter people. It deterred us, although on the other hand we were just trying to encourage voter turnout, not on a holy mission.
Absolutely call the police. Call them this time and make a complaint to get it on record. If it happens again, call again. Keep documenting it. Local laws vary on what kind of canvassing is allowed (generally anything political or religious is protected though, it's considered a first amendment right). And don't let yourself be discouraged, but you might find they're on your side--they probably have gotten other complaints about aggressive church folks like that.
As a general thing, don't go with a plain "no soliciting" sign. If you don't want to be bothered by political or religious canvassers, say that explicitly on your sign (they do make them, and we at least mostly respected them--I always did). I can't tell you how many doorbells I rang that said "no soliciting" and were actually really supportive and happy to talk to me, because they just didn't want salespeople. I would imagine it's the same for religious people. Also, for those of you who work at home or have a young child sleeping or work nights and are asleep, a note to that effect on the door will usually be respected by canvassers. Again, may not apply to people on a mission from God but you'll cut down on a lot of doorbell rings.
Anyway, good luck. Sorry if this information is too general for this forum, but I thought it might help to hear some things from the perspective of someone who did go door-to-door.