shepherdless:
Babylonian tablets record events in some years of Nebuchadnezzar’s reign, but the relevant tablet or tablets from (going from memory) the 11th to 20th years have never been found. The event isn’t mentioned by the Egyptians etc, either. Thus there is no record of the event outside of the Bible. Therefore 586 or 587 is not the “secular” date. It is the one and only biblical date. There is no “secular” date because the event didn’t occur, as far as secular history is concerned.
Though it is wise not to automatically trust religious texts as historical documents, it is a false dichotomy to dismiss out of hand the Bible's description of these events during the Neo-Babylonian period as 'not secular'. Also, automatically concluding that all parts of the Bible are unreliable because some parts are is a fallacy of division.
Stripping away the religious bias of the text, the core description of the events of Jerusalem's destruction is consistent with Nebuchadnezzar's activities in the region during the Neo-Babylonian period. Hence, while there is insufficient corroboration to say it definitely happened (or happened as stated), nor is it entirely without basis.
It is of note that the interpolation at Jeremiah 52:28-30 appears to be from a Babylonian source. Whilst the rest of Jeremiah chapter 52 is copied from 2 Kings, these verses are a separate addition. Also, unlike the rest of the book of Jeremiah, these verses do not count accession years.