The count is not being done by Jews. There is no isur for non-Jews to count.
What is the halachic basis, if any, that allows a Jew to allow himself to be counted (by non-Jews) by actively cooperating with such count?
The last four included Jews among the counted.
Who said that, it having been done, was halachicly correct? And who said the Jews were willing pariticpants in it, in any event?