Relativity is a perfect example because it made very specific and testable predictions such as gravitational lensing, frame dragging, gravitational redshift, and gravitational radiation.
That said, the philosophers of science who originally discussed falsifiability have gone on to say its inadequate, and a huge chunk of work that's published and funded as science these days isn't strictly falsifiable.
Science is a word like any other, that we all agree on to make meaning. Right now lots of practicing scientists work on a definition that includes but isn't limited to falsifiability, but of course the great thing about it is you're welcome to decide what criteria is most comfortable to you. I like to think that the work Einstein did on Special Relativity before 1915, that wasn't mathematically distinct from Lorentz or Poincare, was scientific even though it wasn't falsifiable.
This might have more to do with how "evolutionary psychology"-sounding theories are presented on Web fora than how they are used in a more academic setting. You can easily run across participants on Web fora who almost admit to just making up shit on the spot that fit with the phenomena that they are presented with, based on their expert knowledge of Stone Age humans.