We really don't use either word. I had to look them up because I've never heard of them before. We'd most likely say something is likely to change than use just one word.

I agree they are uncommon. I've only seen "labile" once, in a psychologist's report, and it was used to describe someone whose temperment was erratic or volatile. Protean is more common but still not common. I believe the word derives from an ancient Greek myth concerning Proteus, a person who could change shape into different creatures. So, "protean" is used to describe somebody who frequently changes appearance or persona. Example: "David Bowie was the most protean of 1970's rock stars." You could also use it to describe someone who is involved in many different areas of business/art/other endeavors. Example: "Protean businessman Elon Musk founded such diverse companies as PayPal, Tesla Motors, and SpaceEx."

Agreed! I've never heard of either of those words.

They are extremely rare in ordinary conversation. I've heard "labile" used only in a technical sense, by doctors and scientists. "Protean" is named for Proteus, the "Old Man of the Sea," a shape-changing sea god in Greek mythology. The ONLY place I've ever seen the term "protean" is a technical term in psychiatry; "protean symptoms" are ever-changing symptoms shown by patients who have an emotional need for medical treatment. This is a lovely description of Proteus in "A Wonder-Book for Girls and Boys," a re-telling of Greek myths by the great U.S. author, Nathanael Hawthorne: --- Hercules stole on tiptoe towards him, and caught him by the arm and leg. "Tell me," cried he, before the Old One was well awake, "which is the way to the garden of the Hesperides?" ...all of a sudden, the Old One seemed to disappear out of his grasp, and he found himself holding a stag by the fore and hind leg! But still he kept fast hold. Then the stag disappeared, and in its stead there was a sea-bird, fluttering and screaming, while Hercules clutched it by the wing and claw! But the bird could not get away. Immediately afterwards, there was an ugly three-headed dog, which growled and barked at Hercules, and snapped fiercely at the hands by which he held him! But Hercules would not let him go. In another minute, instead of the three-headed dog, what should appear but Geryon, the six-legged man-monster, kicking at Hercules with five of his legs, in order to get the remaining one at liberty! But Hercules held on. By and by, no Geryon was there, but a huge snake, like one of those which Hercules had strangled in his babyhood, only a hundred times as big; and it twisted and twined about the hero's neck and body, and threw its tail high into the air, and opened its deadly jaws as if to devour him outright; so that it was really a very terrible spectacle! But Hercules was no whit disheartened, and squeezed the great snake so tightly that he soon began to hiss with pain.

If you used these words in a conversation, nobody would know what you meant. I have never heard of them before (and score 99th% on vocabulary). I would agree that using these words would simply confuse your meaning to your intended audience. They are cool if you like studying odd, eccentric English words and their etymologies, but you could go a lifetime without those two words.