They make some where you attach a device to the dog's collar, and it unlocks the door when they approach.

That being said, I grew up in an area completely surrounded by trees and every animal imaginable (squirrels, rabbits, coyotes, raccoons, opossums, deer, etc). We had a dog door (a simple plastic flap) to our barn. I saw raccoons and squirrels with nests literally 10ft from the dog door. Nothing ever came inside. The barn even had food (dog food, plus a fridge and cupboards with snacks). It was even heated during the winter. Nothing came in. I don't know the reasoning, but that little piece of plastic kept everything out.

I would guess that the smells and activity from the dog would keep a lot of the critters out. Most wild animals avoid dogs and don't want to risk getting trapped in an unknown space with one. Not that it will always work, but I bet the critter traffic is vastly less than if the house was left empty with a dog door.

Somewhat related, many of my neighbors have had issues with rats. I have seen them on the edges of my yard but never seen or heard one inside. I haven't done anything to prevent them except for having two indoor cats. These are fully domesticated chubby cats that probably couldn't catch a wild rat to save their life, but I suspect their presence deters rodents for the most part.

I'm not sure. I live in the city where everything is dead! Plus it's extremely hard to get into my backyard (gated complex and high cinderblock wall).

I don't think rodents and bugs are typically a problem though. People, maybe, but if someone wants to break into your house it's not hard to do so and the lack of a dog door isn't going to stop them.