" If so, there will always be some as things like bibliography entries will be the same in different papers"
Beyond bibliography entries, there are fields where it is quite common to have significant portions of a paper contains entire paragraphs that show up in software like TurnItIn. Law and policy are two salient examples. Law papers often cite legal sources (e.g., court cases, statutes) which result in false positives through that type of software. Similarly for policy, where you find artifacts like UN documents popping up in numerous works.
In these cases it is painfully obvious that the results being returned by software programs are benign, and editors don't even raise an eyebrow.
No definite percentage, it all depends on the publisher. However, plagiarism is not tolerated and in some Publishers, once your % is up to a particular rate, like 15-20% (and above) you may be banned for some years from that journal. This is strictly followed in many high-rated journals, I don't want to name here, all the same, be as original as possible and bear in mind that high-ranked journals have sophisticated software far better than those free online ones to rake your script.
The bottom line is, be as original as possible in your write-up. Your paper is your image.