Kuhn's work marries Sociology to Scientific Progress (i am not sure whether you have actually read the book; it is a difficult work to comprehend) and his thesis is often used by the anti-science crowd to argue that Scientific Facts are merely Social Constructs rather than Objective Truths. While the process of doing science and its progress are subject to sociological pressures (i.e. subjective) the theories/models arrived at are objective truths (for the hard sciences) and verified by employing the scientific method (mainly by peer review and experiment replication). But Kuhn argued against Scientific Realism (https://en.wikipedia.org/wiki/Scientific_realism) and instead proposed Scientific Paradigms (i.e. normal science as puzzle solving within a shared set of beliefs) and Scientific Paradigm Shifts (i.e. revolutionary science due to changed evidence and hence beliefs). This is what is exploited by the anti-science crowd to argue that nothing is definite and everything is subject to change since they are all "just beliefs". Note that Poincare's works on the philosophy of science gives more necessary background.

Contrary to your claim, anti-science does have methods/processes/techniques since it is a movement(s) with a definite goal(s). Wikipedia gives the details - https://en.wikipedia.org/wiki/Antiscience

What don't you understand from my statement "Scientific awareness does change the outcome; just not 100% and not all at the same time."? It is self-evident if you had actually read Kuhn or Poincare. The "outcome" referred to is the acceptance of scientific theory/model under discussion; "just not 100%" means all aspects of the theory/model might not be accepted initially pending further experimental validation and "not all at the same time" means the acceptance of the theory/model happens over a period of time.

> The trouble is science doesn't have tools to prove counterfactual "if science was unaware the outcome would be different". This problem affect my opposite statement too: we can't prove that outcome wouldn't be different.

This makes no sense at all. The various scientific theories/models have changed people's lives, civilizations/world etc. most definitely. It just happens over a period of time as more and more people buy into the new theory/model and/or see proofs of its correctness via technological advances.

As regards your last few lines w.r.t. sections of the anti-science crowd; it is easily explained by agendas (religious, political etc.), propaganda and plain old stupidity/pigheadedness. As the ditty goes; if you have the facts on your side, pound the facts; if you have the law on your side, pound the laws and if you have neither, pound the table.