How common is it for a science research paper to include direct quotes? Is there a consensus that direct quotes should never be used in such papers?
I guess I disagree, but you have to think about what you are doing. Anytime you use another's words directly you should quote them and indicate explicitly that it is a quote. This can be done with "quote" marks or otherwise, such as indentation. You also need to provide a reference to the source, say, in a footnote. 

However, perhaps your professor is saying that, rather than quoting people's words directly, you paraphrase their arguments, etc. instead. Then you don't quote them. You still need the  reference, of course and need to be sure that your paraphrase is accurate. Your formatting, etc. needs to make it clear that the words are yours, not theirs. 

But I would suggest you explore it further with your professor. Perhaps he or she has another idea in mind.