Not rural myself, suburban/city, but it's easier than you think, and you sort of . . . learn the animals around you, I guess?

In my area, I see coyotes pretty frequently, and see their scat all the effing time (so far, four times today). They're clearly around. They're also basically harmless and easily scared away. They are a danger to small animals though, so my neighborhood doesn't have a lot of 'outdoor' cats, and small dogs need to be in yards or on leashes. Generally the coyotes come out at night, so you just won't interact with them. Similar to foxes, really.

Bears are scary, but uncommon. Black bears are dangerous (they'll try to take food, they can decide to attack people, they're kind of smart) but can be scared off. Brown bears, luckily not in my area, mostly you get away from brown bears but they will sometimes just ignore you.

American Alligators are chill. (Crocodiles are not.) We have lots of alligators and very few crocodiles. As long as you are not being dumb, you're fine around alligators. Kind of rough to fish around them, and keep small pets and small children away from the bigger ones, but they aren't nearly as dangerous as you probably think. They're also fairly smart, and anything under about 3 ft is going to chose not to fight a whole grown person. If you look at American Alligator attacks on humans, it's almost always an alligator attacking a small pet near water and the human jumping in to the fray to save their dog and then getting bit. They can totally kill a human, but they rarely, rarely attack and they just don't want to, you know? We aren't their food, we're also too big for most of them and fight back. If you ever come to the southeastern US, I highly highly recommend going on a 'swamp tour' so you can see alligators from a safe distance, they are amazing animals, and we really lucked out with our particular crocodilian species.

Snakes are a little harder, in that they are common (in my area) and not as easy to see as the other dangerous animals. Probably the most dangerous animal I see regularly is venomous snakes (mostly rattlesnakes, sometimes Cottonmouths), I'm decent at id-ing snakes, and most of the ones I see day to day are harmless, but I see Western Diamondback Rattlesnakes pretty often, and those are the #1 when you look at actual bites. The thing with snakes though, at least USA-snakes, our venomous snakes may not all be scared of humans, but they don't want to fight something so much bigger than them. They'll typically freeze, make some kind of warning gesture at you, and wait to see what you do. So what do you do? You go around them, with a good cushion of space, and everyone lives. Don't approach a venomous snake, don't try to move a venomous snake, leave them alone and they'll generally leave you alone.

Now, the worst animal? Wild boar. I see these a few times a year near my house, almost always while safely in the car, but these are dangerous and aggressive (and not native). If I'm out hiking and see signs of boar, I will leave the area. They're aggressive, they're also pretty fast. It's always 'open season' on these, because they have no good side. You report these, and someone will come out and try to kill it.

Oh, and mountain lions. Pretty rare to actually see in the wild, it's only happened to me once and I about had a heart attack. We locked eyes for a second and then she (?) noped out of there. Beautiful animals, they will generally hide and you'll never know one was nearby.