The trails and signs are there for a reason. Respect them!
When driving a boat or a car, off-roading in sensitive habitats like grasslands, mangroves, salt flats, swamps etc. can be disastrous for ground-nesting birds, fish schools and scores of plants, insects, and snakes. It can also cause immense damage to the habitat itself.
And this also applies to being on foot. That is, stay on paths/trails. They’ve been designed for a reason: to keep you as well as the wildlife and its habitat safe.
As for the signs, respect them. Not doing so might simply result in death! Here are two recent unfortunate illustrations of this: After a toddler felt in the enclosure of Harambe, the Cincinnati Zoo took the decision then to kill the peaceful gorilla to ensure the boy would not be harmed even inadvertently [AN16]. A few weeks later, a 2-years old child was killed by an alligator at a Disney park in Florida [LR16].
We should all apply a degree of common sense: If we are in territories where wildlife and especially potentially dangerous wildlife abounds, we should proceed with caution regardless of whether there are signs or not and take responsibility for ourselves as well as the animals.