I don’t think I’d like to meet the Einstein who would need to be told that literally. 
Heck, even sea cucumbers know to scurry away after pooping.
This pretty much covers it. Personally, I would use “don’t fish in the company pond” for a work related situation. I’m classy like that.
Not that a lot of people take the advice. Work hookups/dating are not exactly rare. It’s not surprising that you could become attracted to someone you spend 40 hours a week with. You do have to weed out the ones you’d like to kill first.
I knew the expression** before I watched The Sopranos, but it’s funny when I first saw this thread, I heard James Gandolfino’s voice saying this in my head.
**And I knew it as a general phrase – not specific to the work/dating situation.
The problem is when you’re attracted to somebody now and you act on it, they may later end up becoming somebody you’d like to kill.
Don’t bother me with details, I want to get laid right now! 
My father, who was quite the pedant, said the derivation of “don’t shit where you eat” simply meant, “an animal doesn’t defecate in it’s own nest,” meaning, more or less, don’t do your stupid/messy stuff where you have to live with it.
As for romance in the workplace, the two phrases I’ve heard the most are “don’t dip your pen in the company ink” and the even more folksy “don’t get your meat where you get your potatoes.”
I’ve always understood the expression as meaning “don’t do something that may have consequences close to where it can have an adverse effect on you, or the people you care about,” Or, "don’t do anything nearby that can come back to bite you in the ass.” It’s quite general and can have any number of varied applications.
Examples:
Don’t make a fool of yourself in your neighborhood, where you’ll give yourself and your family a bad reputation. Make a fool yourself somewhere else, where nobody knows you.
Don’t steal from the company you work for, steal from some other company, where you won’t get fired if you’re caught.
Don’t shag your girlfriend’s friends, shag someone else, where word won’t get back to your girlfriend and she whoops you upside your head.
And so on and so forth.
I have heard this expression going quite far back. It always, 100%, meant the “don’t have an affair at work” thing.
It’s an analogy. It’s not intended to be taken literally. Consider “Don’t bite the hand that feeds you.” No one should interpret that to mean not to bite someone who is giving you some actual food.
No offence, but should you invite me to dine at your house, the answer is no.
It’s probably an older expression than the more recent reevaluation of workplace relationships.
It really doesn’t make sense, for workplace relationships. OK, work as “where you eat” isn’t too strained, but shit is a lousy metaphor for romantic relationships. Or at least, it might be a good metaphor for some of them, but nobody ever thinks they’re in one of them, while they’re in it.
And there are enough other contexts where it does make sense (like illegal activity), and enough other sayings that do make sense for workplace relationships (I’ve also heard “don’t get your honey where you get your money”).
Agree. The relationship gloss seems slightly off to me.
Likewise. The idea it’s primarily about office romances sounds nutty to me.
Are they an example of an activity that fits the general point of the saying? Sure. If you work in a big ol’ cube farm are office romances probably the circumstance you’ll hear this applied to the most? Probably. But that’s just speaking to how narrow a social sample a cube-dweller gets to experience
I think the metaphor works fine for an adulterous affair, or for a “player” who is only after casual sex that may be emotionally harmful to the person they seduce. But for normal dating, I agree with you. It may be a poor idea to date cow-orkers, but the “shitting” metaphor is inapt.
In the Sopranos, Tony also used the expression in the sexual sense when he went to Italy and could have had an affair with the woman mob boss, but he told her, “sorry but I don’t shit where I eat.”
This seems very wise and fits the OP’s theme.
This reminds me of an incident involving an unwise thief, who was driven to steal from his neighbors, including me, by his drug addition. Eventually he was caught–not very wise, he–and 66% of our stolen possessions returned. He definitely learned the lesson of not shitting where he eats.
Another variant of this idea is “don’t dip your pen in the company ink.”
From re-reading some replies, I think we may be missing an important distinction in the “office relationship” definition of the phrase. I’ve heard it in regard to illicit affairs in the office - not two co-workers openly dating, but a married person cheating, especially a married boss carrying on with a subordinate.
Earlier this week my coworker said, “He (team lead) should not shit on the plate he uses to eat.”
Seems to be the literal English translation of the equivalent Italian expression. And my coworker was talking about a married person carrying on with a subordinate. Team lead is no longer employed due to his craptacular behavior.
Come to think of it, I think this expression was the original argument for the Clean Water Act.
I still maintain that the idiom has a more general application than some of you believe. I think the Wiktionary definition is apropos: “One should not cause trouble in a place, group, or situation in which one regularly finds oneself, as it will likely backfire.”
Office romances may be the most common application of the term, but not the only one.