When scripture quotes a non-biblical source, without any opposition of the source, does it imply any endorsement? In addition to alluding to various Jewish proverbs, sayings, and parables, sometimes the Bible seems to directly quote Greek philosophers (Acts 17:28), Jewish oral traditions (Jude 9, 12) or possibly even  pseudepigraphal works . 

Under a biblical framework that holds to the infallibility of the Protestant Bible how are we to approach those extra biblical sources being quoted?  Does the scriptures reference of them pass on some kind of dignity or validity to them, or is a extra biblical reference in the scripture neutral not to have higher esteem than it otherwise would have? Or would each case have to be considered on its own and if so, under what guidelines?
I'm hesitant to give an across-the-board answer, but there is a well-established principle in understanding Scripture that applies somewhat here.  It was included in an earlier answer of mine addressing the question of what we are to take literally as opposed to figuratively in Scripture, from a Fundamentalist standpoint.

First:


  
  [Because the Bible is inspired, it is inerrant, infallible, and authoritative][2].  No word of fallible man can stand in authority
  over Scripture.
  
  Scripture is intelligible. God meant for us to understand it.
  Because it is infallible, the Bible is internally consistent. it can't contradict itself.
  Because God meant to communicate truth, and because Scripture is internally consistent, the words of Scripture have only one meaning in
  context. There may be multiple legitimate applications of a passage of
  Scripture, but a passage has only one meaning in context.
  
  


Then, the part that I think applies here, important bullet point bolded for emphasis:


  Dr. David L. Cooper, the founder of The Biblical Research Society
  out it much more simply.  Dr. Cooper is known for his “Golden Rule of
  Interpretation” which is as follows:
  
  When the plain sense of Scripture makes common sense,seek no other
  sense;
  
  Therefore, take every word at its primary, ordinary, usual, literal
  meaning unless the facts of the immediate context, studied in the
  light of related passages and axiomatic and fundamental truths
  indicate clearly otherwise.
  
  so, from this quote, from Dr. Cooper's perspective,  we see that we
  are to take Scripture at face value (literally) unless...
  
  
  The immediate context makes it clear that the passage is not to be taken literally.
  Related passages, the literal sense does not make sense
  The literal sense of the passage would contradict axiomatic, fundamental truths.
  


That last principle can and should, from a Fundamentalist Sola Scriptura, Biblical inerrancy be applicable to anything questionable:

Does the passage contradict axiomatic, fundamental truths

If the Bible includes a passage, and doesn't oppose it in the context of the surrounding verses and doesn't contradict axiomatic, fundamental truths, then we can say, at best, that the author isn't opposing the statement, that it's not doctrinally incorrect, and that it's not blasphemous.  I don't think we can go so far as to say Scripture (or the author of that particular passage) endorses the idea, unless it is clear, within the context of that passage that the author is endorsing it.