Scientific pursuit of truth
I'm reading a Philosophy of Science book by Abraham Kaplan called The Conduct of Inquiry: Methodology for Behavioral Science with some colleagues at school. Kaplan borrowed from John Dewey when he stated the autonomy of inquiry principle as a declaration of scientific independence in his opening paragraph.
It is the principle that the pursuit of truth is accountable to nothing and to no one not a part of that pursuit itself.
This is an idealistic position because scientists are held accountable by many sources whether regardless of legitimacy. My question is whether the same principle applies to religious truth-seekers? Are we only accountable to others on "the quest"? Even if the answer is yes, it's rarely a satisfying response to critics.

Having not done that reading, I'm not sure I fully understand the statement. However, blind ignorance should not keep me from taking a stab at your question.
While that statement may be quite true of some religious orders, that seems too insular to be a proper expression of someone who takes Matthew 28 seriously. How does one be accountable to others on "the quest" without encouraging others to join the quest? That requires an outward view.
The principle, as applied to Christianity, doesn't suggest we be insular and cast aside the Great Commission. Rather, it states that Christians are only accountable to other believers in terms of the pursuit of truth. In other words, Christians don't have to worry about what non-Christians say about Christian beliefs. Obviously, we as Christians are accountable to non-Christians in many aspects of life, such as work, school, and friendships. The question is whether we're accountable to them for the judgment of truth. I think the implicit attitude among Christians is that we're not accountable to anyone but God and our brethren.
That attitude may function well for theistic truths or beliefs, but I think it runs into trouble when it's applied to truth in the natural world. If Christians claim a miracle, they should be able to support it with evidence to anyone who asks, including, and perhaps especially, non-believers.
First off, it's quite evident that the quote is from a philosopher. Once you get your head out of the clouds and realize that such a pursuit must take place in the reality of society as Chris mentions, there are many individuals and institutions that "truth-seekers" must be accountable to.
It's also clear the limited applicability of this statement to science. The pursuit of knowldedge through science relies very much on accountability.
The wording is interesting in the quote relative to science and religion. The use of the word "truth" is commonly used by religion/philosophy whereas science often uses the word "knowledge" when speaking of high level goals (e.g., pursuit of truth/knowledge). Both are an attempt to understand and yet I think this subtle word choice hides how different each path is.
Anyway, from a scientific perspective, the quote is silly. If it's not clear how it's silly, more can be said. From a theistic perspective, it is also quite ridiculous as I agree with Dave in that it suggests a very insular perspective. Without accountability to current non-believers of the truths Christianity believes it possesses, it has no hope of persuading new believers, through intellecutal or emotional persuasion. The pure and total adoption of such an elitist perspective by any religion will result in its own extinction. Without "the great commission" or similar objectives to grow its numbers, a religious body will gradually die out (the number of ways it could "die out" are many).
That was my objective response. My subjective response is that it is shocking that any religion would even struggle with such an issue. Such a struggle suggests ownership or exclusive rights to truth/knowledge without any obligation to explain, justify, or prove the "truth" to others. This righteous type of behavior breeds emotional contempt and intellectual disrespect. Neither is good for Christianity or any religion. In fact, when both emotional contempt and intellectual disrespect are stimulated, you've most likely created a dangerous adversary.
John Dewey got the autonomy of inquiry principle right when he said, “It is the principle that the pursuit of truth is accountable to nothing and to no one.” Why add, “not a part of that pursuit itself”? That’s not an autonomy of inquiry principle; that’s a limited autonomy of inquiry principle! Dewey limits the autonomy when he implies that people pursuing truth are accountable to other people pursuing truth.
It’s fine with me if Dewey both pursues truth and considers himself accountable to other people who are also pursuing truth. But if he lumps together a statement of autonomy with an implied statement of accountability, then he is either limiting his statement of autonomy, or he is stating two separate principles.
The question, “are people who pursue truth accountable to other people who pursue truth?” is separate from the issue of calling a principle what it is.