I figured out that only the sort order that is active at open of the file is used for export sort order. Changing the sort order by tabs doesn’t affect the export sort order anymore!
One example:
- Options… File… Export sort order: “Use current table sort order”… Save
- On opening, table is sorted by Date (descending)
- File… Export… Export all entries (same for selected entries!)… Filetype: HTML (e.g.)…Filename: arbitrary… Save
Result is OK - Sort table by Date (ascending)
- repeat step 1 (different file name)
Result: Entries are still sorted by descending date - Sort table by Author
- repeat step 1 (different file name)
Result: Entries are still sorted by date (descending)
Workaround: Sort table e.g. by author… close Jabref (saving the bib file not necessary)… open Jabref with last file (still sorted by author)… export… Result is sorted by author 
Haven’t tested, but is for library option “save sort order”, there might be the same reason that causes problems.