The non-Newtonian denotion is not about Newton's 3rd law. It is just a referral to the, shall we say, "expected behaviour". And such "expected behaviour" is that when you push harder (shear stress), the liquid moves out of the way faster (shear velocity) proportionally or linearly.
By DirectEON (talk) 08:46, 28 March 2008 (UTC) - self-made, CC BY-SA 3.0, https://en.wikipedia.org/w/index.php?curid=16635877
Water is (basically) Newtonian. But substances like quick sand, paint or toothpaste are obviously not, since they for instance become unproportionally harder under load (so a quick jerk in your leg will only make it more stuck) or become less viscous (more "flowing") under load (that is why you stir your paint bucket and squeeze your toothpaste tube) and so on.
I believe the term "Newtonian fluid" has been coined due to Newton being one of the first to try to describe liquid behaviour under stresses via differential equations with originally linear solutions.