It does appear that Assignee and Due Date are forced to be the 1st 2 columns regardless of order of columns in the template.
Also, having the same issue. Our workaround is to reorder the columns then save the view. We have about 200 projects that need to be created all at once and the work around of manually re-ordering will create a significant delay for our teams.
This never used to be a problem, but I am now also having the same problem: the Assignee and Due Date fields are #1 and #2 in the template, but when I create a project using the template, they get shifted to #2 and #5 respectively. Navigating to a different view and back doesn’t solve the problem. I have to manually drag them and then ‘save view’. This has been a sudden change in the last few weeks.