A example of unscientific research which I personally find inspiring, which ended up turning into proven science was the work of Australian Dr. Barry Marshall and Dr Robin Warren.
Even though conventional thinking and the remainder of the medical fraternity believed that the stomach was too acid to support bacteria, Drs MB/RW believed that some gastric/peptic ulcers were caused by the bacteria Helicobacter pylori. At the time these doctors were ridiculed by their peers who thought that they were unprofessional through to outright crazy.
While the evidence was not overwhelming about the causal link between Helicobacter pylori and ulcers, the Drs MB/RW thought that there was potentially a sufficient evidence that a link may exist and it was worth testing. As part of testing, Dr BW chose be the subject of his own experiments and decided to consume an elixir containing Helicobacter pylori. He became very unwell and developed the early stages of an ulcer infection.
As it was also known at the time that Helicobacter pylori could be controlled using conventional antibiotics, Dr BW treated himself to cure the emerging ulcers.
Drs MB/RW unscience ended up becoming renown and celebrated science, which may have been the precursor to the discovery that viruses and bacteria can cause human ailments, such as heart conditions and cancer.
The cure for forms of peptic ulcers was a significant medical discovery because previously the symptoms of the ulcer could only be treated and the ulcer being managed. The cure provided a permanent relief for those who has been struck down with the debilitating condition.
The Drs have also won a Nobel Peace prize and are also recognised as some of the top influential people in the world. With persistence and challenging the norm, they also managed to change the views and opinions on many on the medical fraternity.
There also also many other examples in history where unscience has been eventually proven to be science, and some which have not been proven to the case. This is one historical strengths of the scientific and research community that one can table different views and opinions, test those views and see if the hypothesis can be proven. If such had no been done for some hypotheses, many of the scientific and engineering advances of the modern world would not have occurred as one would have been reluctant to voice a differing view to consensus, with fear of being ridiculed and ignored.
Challenging the norm, whether based on evidence or a ‘hunch’, drives innovation and the testing of theories or solutions which may otherwise been the case. It also leads to changes in opinions and thoughts.
There is a role for unscientific research in the scientific community, but when this leads to conspiracies or blatant falsehoods (e.g. antivaccination groups and @postulative example above), they should be challenged with appropriate evidence.