Keep the safemode on.
If necessary, blacklist troublesome animals so you noticee them before they are on top of you
Keep an eye on your compass notifier too.
Also I suspect you are assuming that the normal window is view radius. This is not so, as using (Z & z) will show you the actual vision radius is to far to be able to reliably see most things.
Use the (V) key to look at entities your char can see, even if outside the zoomed view (tab to switch between items and entities)
Or you can use the (
key to look at things, including those outside the current screen.
If the creature is showing tracking then it is time to start © yelling at them like Gary Busey with tourettes. Animal Empathy makes it >less likely< an animal will attack you. This isn’t especially helpful against naturally hostile animals that want to eat you/ have some motivation besides not liking your face and the way you walk. Such as wolves/dogs that want to eat you. And the stupid territorial moose that will defend its territory against offensive minivans.
Think of Animal empathy like it gives you more buffer space before aggression will take place, not a “animals believe me Cinderella and will do my laundry while a whistle in their ears and pet them.”
Somehow a yelling man BEFORE they become aggressive is usually enough to frighten them off though. I think After they become aggressive will work too, except it usually takes longer to scare them off, then it takes for them to shred your face off.
