Do you swerve? Animal in the road, no oncoming traffic.

Why is this an issue? What kind of person deliberately runs down an animal when they can avoid it? That shows a very low, even malignant, character.
This has nothing to do with safety. If the object (living or otherwise) can't be safely avoided, then you hit it. Unless it's a person, then I'd push the safety envelope all the way, out of instinct, as all non-sociopaths would.
The only reason this comes up is because companies tell their drivers to do it. But is that how you decide what is safe or right - whatever some youngster who has never done your job tells you to do or what some "policy manual" tells you to do? Of course, I have spared the life of a couple deer and other assorted furries; I know what I'm doing or can do with my rig at any given moment - no one else knows, only the person driving.
You, the driver, are the final arbiter of what you can do safely. My company repeatedly tells me, "never make a u-turn because it's unsafe" ...see what I mean - why would I listen to them?

 

I guarantee that animal will follow you into the other lane anyway. It will try it's hardest to commit suicide no matter what you do.

 

When it was safe to do i have stopped and carried small critters to safety.