That's a big oversimplification. Project Orion-style propulsion is certainly not ruled out by our current understanding of physics. There's no non-Newtonian mechanics involved, just the substitution of a nuclear reaction instead of a chemical one. Not to mention that we have lots of evidence of non-Newtonian mechanics (e.g. Special and general relativity), even if whether GR can assist in space travel is an open question.

If look at it the other way around: burning the reaction mass is the only source of energy you use to accelerate the reaction mass — it doesn't sound obviously optimal.

Nuclear thermal, and nuclear/solar electric (aka ion) rockets achieve better specific impulse despite carrying separate weight for power. Some nuclear designs (e.g. Orion as johncolanduoni said) do have overlap between reaction mass and energy source mass. Solar sails, ground lasers, and gravity assists avoid some of the need for carrying reaction mass. All these are perfectly newtonian.

Chemical does win among currently working designs at accelerating quickly, which is critical for human exploration, and to some degree for getting to orbit. There is no inherent physical reason alternatives can't achieve that.

I must recommend the extremely fun Project Rho site though I'm just started reading it: http://www.projectrho.com/public_html/rocket/enginelist.php It's not always clear where existing science ends and Sci-Fi begins, but that's generally on technology barriers (e.g. we haven't yet managed break-even contained fusion), not mythical "entirely new understanding of physics". And the amount of actual science — detailed papers, prototypes etc — on diverse and bizzare drive designs is way more than I expected!