Is there a theory in biology that was initially disregarded as false (because of critical or contrasting perspectives) and only recognized as important after a considerable time, possibly only in recent years, thus significantly impeding its development?
The idea that organisms with mitochondria derive energy from respiration through a proton motive force was considered controversial at the time.
This is the best reference I could find at the time:
His theory explained that it was the energy captured from those protons returning to the matrix and not energy stored in an undefined high-energy covalent chemical intermediate that was then used to drive ATP synthesis. This Nobel Prize-worthy concept (1978) was so counter to the leading theories of the day that the field spurned it for the better part of a decade.
Pagliarini, D.J., Rutter J. Hallmarks of a new era in mitochondrial biochemistry 2013 Genes Dev.
The idea that life is not spontaneously created, but always develops from... well, something.
For decades, centuries even, the notion that invisible micro-organisms were responsible for diseases, mold etc. was controversial.
Louis Pasteur's swan necked flask experiment (in the 1860's!) is one of the last and most famous demonstrations that sterile media must be contaminated and cannot generate life from scratch. He showed that a sterile broth communicating with the outside world through a single aperture was not contaminated if the aperture was long enough to prevent accidental contact with ambient micro-organisms, whereas the broth grew turbid quickly after being directly exposed to air by removing the swan neck.
Before this theory was accepted, the notion that sterility is important notably in hospital settings was often challenged, leading to thousands of people dying of nosocomial infections.
I notice from his bio, that the poster is a mathematician, so I have chosen to answer this question as an experimental scientist (a molecular biologist with a chemical education) to a non-experimental scientist:
In my view, for biology, the acceptance or rejection of hypotheses plays only a minor role on the development of the science. This is because actions speak louder than words — it is the experimental validation or support of a hypothesis that is important. If the hypothesis is correct, but the technical or theoretical basis does not exist to test it, then that basis is also lacking to exploit the idea.
This only applies to an open society. An example of the damaging effects of false theory can be seen in the rejection of genetics by the Soviet Union in the 30s (and later) on political grounds (Lysenkoism), a rejection that did not affect science in the West, but was responsible for thousands, if not millions, of deaths by starvation because of its influence on Soviet agricultural practice.
Let us consider the two answers already given (both of which I have upvoted). First @Mowgli on Pasteur and ‘germ theory’. I would maintain that it was only when a mode of killing ‘germs’ by heat was suggested, that practical demonstrations of the effectiveness of measures to prevent spoilage of food and drink (and to prevent sepsis) was possible. And it was these practical demonstrations that overturned the prevailing theories, not the strength of the intellectual arguments against.
The case made by @Cell for the rejection of Mitchell’s hypothesis is perhaps more pertinent. Certainly Oxford biochemists were still taking about X~P (an unidentified ‘high-energy’ phosphorylated intermediate) in the mid 60s, five years after the hypothesis was published in Nature. But the key — and unusual — thing was that this was specifically a hypothesis. It was supported by a variety of arguments and equations, the latter of which would cause many to shrug their shoulders. Clearly some scientists were attracted to the idea, but it took a system with photosynthetic bacteria to provide practical evidence, as well as improved characterization of the membrane ATP-synthase (which was generally referred to as an ATPase, because that was all it could do in vitro). So the maximum of a 10-year lag in acceptance was not caused by the rejection of the idea, but the lack of a means to prove it.
Similar arguments may be made about the non-acceptances of the idea of Avery (1944) that DNA was the genetic material. Although this was based on experiments, one could argue against the experiments. It was only with the determination of the structure of DNA and the development of phage and isotopes, that the means to confirm this idea and develop the field further arose.
That’s how I see it. However I would be interested for suggestions of any other examples (template theory of antibodies?).