No, bad idea.  Biological sex on your ID is one very clear identifying feature that works for the vast majority of people.  It stays.  As for adding gender, again, this has some advantages, but maybe disadvantages.  It is unfortunate that many of the worst examples go back to 1940s Germany, but here goes: At least one conquered county listed religion on passports/ID papers and you can imagine how that was used against the citizens who were Jewish.  In a world where tolerance is not universal, do you really want gender on a passport?