I would like to provide a counter example showing that belief in crazy ideas doesn't always mean the end of your career. I did my PhD research in the Stanford Biochemistry Department, which was home to Arthur Kornberg; Nobel laureate for his discovery of DNA Polymerase. In his later career, he became obsessed with inorganic phosphate, which he felt was the key to understanding the origins of life. His evidence for this was far from convincing (many said laughable) and every year when the faculty would introduce their research to new grad students, you could see all the other faculty cringe as he would introduce his lab.
Despite his eccentric views he was still well respected and frequently asked to speak at other universities. When he did, he refused to talk about anything other than inorganic phosphate and if anyone tried to get him to talk about DNA Polymerase, he would call it a "former distraction" and refuse to talk about it any further. This meant he didn't get a ton of repeat speaking engagements, but he still gave lectures, still was an active researcher in the Biochemistry Department, and still found students willing to research in his lab to have a Nobel laureate on their CV.