Should scientists be free to research whatever they want, assuming it does not harm/hurt anyone or animals.
No. Science is a community with rules and an ethos of consensus and coherence. The choice of research topics is a choice with an ethical dimension and, practically speaking, impinges on limited resources. While the range of viable research topics may be very broad, it will be limited in some sense if the coherence and effectiveness of "science" as a practice is to be maintained.
If a lone "mad scientist" retreats to his castle to research something that is nonsensical, ignores the current state of the field, or is somehow evidently despicable, it is questionable whether we still call that person a "scientist." Many actual research projects can and do harm people and animals, with arguably some greater good in view. That is a different issue.The more relevant limitation is that of meaning and coherence within the discipline.
This is an opinion-based question, so I'm addressing facts that should be considered in any possible answer.
Investigation is the task of gathering knowledge. Any negative answer would imply that some knowledge is forbidden (personally, I don't agree with this perspective, so I personally find @NelsonAlexander's position incorrect).
Investigation is not related with the scientific method, which might relate investigation with experimentation. Experimentation do has ethical rules. Not investigation.
The goal of investigation is to get knowledge. Knowledge is used for survival. Any possible knowledge is useful: that's why this can't be forbidden. Knowing if drinking water allows survival, is as valid as knowing that drinking poison causes death.
Investigating anything, including pseudosciences is just producing knowledge, should not be prevented. Knowing that there are no scientific proof that tarot causes earning more money is useful
Any prohibition would imply a subjective position of what to forbid and what not. A corporation might implement that, given that the subjective position is determined by the owners, but if a society would do this the result would be a "Bureau of investigation rights". Quite like Cuba or Laos, in other words: a dictatorship, a censorship.
Multiple remarkable scientists in history have investigated weird things, and that can't be considered improper. They just found information that is still useful for society nowadays.