To be honest, while I do tend to lump things together myself, for convenience, science is not a monolith. And, you are right that the idea of the scientific method is flawed, at times - it works for some disciplines but not for others, which develop their own system.
But, the one constant is that there has to be debate and testing of ideas - from within your discipline but also from other areas to avoid echo chambers, especially when there is now such hyper-specialisation and very narrow fields of research.
And, on the level of individuals and groups, it is still important to question and analyse, and be sceptical while also open to ideas. That applies to scientific debate and to public debate about science - at the end of the day, science is very much a public concern, and the public has a stake in it. If science only happens behind closed doors with everybody else shut out, then we are screwed.
Censoring science goes against everything I stand for - much better to make them defend their position.
A quote you may like from the great Carl Sagan: