Many creationists and intelligent design proponents put in a lot of time ‘refuting’ ‘Darwinism’.
I think the ending ‘ism’ is unfortunate, since it suggests an ideology rather than a scientific theory. (I’d be happy to use the term ‘creation science’ rather than ‘creationism’ for the same reason.)
But it’s more than that: Darwin got a number of things wrong. Mendel’s work on the gene concept was published some years after the Origin of Species, so Darwin was working without the gene concept, without knowledge of DNA and with a vastly smaller body of evidence than modern scientists.
‘Darwinism’, therefore, in any pure sense, is rejected by modern evolutionary biologists. There is little mileage in refuting it.
Refuting the ‘modern evolutionary synthesis’ is more complex, because that set of theories is deeper and more complex. There’s probably a whole other post in discussing Karl Popper’s concept of scientific theories as ‘conjectures and refutations’, Thomas Kuhn’s ‘scientific revolutions’ and Imre Lakatos’ advanced modification of Popper’s ideas as ‘hard core and protective belt’, but that’s not for this time.
I’m hoping that, in the spirit of peaceful science, it’s a useful suggestion to avoid talking about ‘Darwinism’ if you’re someone who is bringing forward a well-considered and thought-through critique of the modern evolutionary synthesis.