In a TED talk (first 2 minutes of the video), Rupert Sheldrake states that the "scientific worldview inhibits free inquiry".
[emphasis added]

For Debate
Does making science into a "worldview" inhibit free inquiry?
 
For Debate
Does making science into a "worldview" inhibit free inquiry?
My answer is yes. Two fields of study that have been subject to restrictions (or attempts at restricting, more the case in the past) have been the field of parapsychology and those that study UFOs. In the case of parapsychology, many scientists have questioned it but some of its critics focus on the subject matter of parapsychology (i.e. telepathy, psychokinesis, etc.) instead of methods. Take for instance, this article piece by physicist Sean Carroll:
The only problem is, parapsychology is not science. It's pseudoscience. From a completely blank-slate perspective, one can certainly pose scientific questions about whether the human mind can tell the future or read minds or move objects around without touching them. The thing is, we know the answer: no. The possibilities have been investigated and found wanting; more straightforwardly, they would violate the known laws of physics. Alchemy was science once, but it's not any more. Not all hypotheses are equally worthy of our respect and attention; sometimes we learn that a particular idea doesn't work, and move on with our lives.
Here we see that Sean Carroll is making the subject matter the issue.

We find the same thing done when it comes to UFOs...
Skepticism and taboo has inhibited research into UFOs. There's no real scientific body devoted to studying UFOs. It wasn't until recent sightings by the US military, that just so happened to be leaked, that now the issue is being taken seriously. Here's an article in the Scientific American that covers this point:
Recent UAP sightings, however, have so far failed to generate similar interest among the scientific community. Part of the reason could be the apparent taboo around UAP phenomena, connecting it to the paranormal or pseudoscience, while ignoring the history behind it. Sagan even wrote in the afterword of the 1969 debate proceedings about the “strong opposition” by other scientists who were “convinced that AAAS sponsorship would somehow lend credence to ‘unscientific’ ideas.” As scientists we must simply let scientific curiosity be the spearhead of understanding such phenomena. We should be cautious of outright dismissal by assuming that every UAP phenomena must be explainable.
(emphasis added)

What is an "unscientific idea" (as opposed to unscientific method) if not something that goes against a scientific set of "ideas" or worldview?

I think these 2 examples will suffice to show how having a scientific narrative or worldview can inhibit what we study. If there's any objection to inquiry, it should be about how something is studied, and not what is studied or whether or not the subject matter goes against current scientific views.

I found one psychologists that explains this best, psychologist Chris French:
In the final analysis, science is a method for approaching the truth, not a body of established facts or a particular set of phenomena. In deciding whether parapsychology is better described as a science or a pseudoscience, we should look at the methods employed by parapsychologists. It would be unfair to judge any discipline only by considering the poorest work done within it (if we did so, psychology would certainly be dismissed as a pseudoscience). Parapsychology at its best—as exemplified by, for example, the articles in the Journal of Parapsychology—appears to meet most if not all of the benchmarks of true science as opposed to pseudoscience. That is so even if paranormal forces do not actually exist.
 
I think it is a case that mainstream scientific research is limited to materialistic pursuits and any study outside of that parameter is considered pointless. Scientific research is generally done where investment is made, re the usefulness of the science in terms of how it might benefit the ones doing the investing.
 
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I also question if free inquiry can exist in an age where politics has a big influence in some societies, like the United States.

Would some topics be banned from being studied simply because it might offend some group? I would at least think that even if the results of studied were stretched or falsified to fit some agenda, that at least independently replicated studies would expose that. But what if an issue isn't even studied?
 
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