Hello yugen: Well... I don't know about this.

For one thing it's not clear to me, from what you wrote, specifically what your position is currently. It sounds to me as though your new manager is viewing you as "support staff" in which case having you do the things he's giving you to do would make sense. But perhaps that's not really your position in the office?
I wouldn't say you're being stubborn. From what you wrote, it sounds to me as though you have valid concerns. However, I don't feel it's your place to go over your manager's head to the district manager, especially since this new manager has only been in the position for a month.
For one thing, going to the district manager is certain to cause untold tension between you & your new manager. Plus... there's no way to know how your overture will be received by your district manager. (And s/he may not tell you forthrightly either. I presume you don't know, for certain, what relationship there may or may not, be between your manager & the district manager.) So for all of those reasons, my feeling is that now is not the time to be taking your concerns to the district manager.
If, as time goes by, you become convinced your manager's actions, or lack thereof, are damaging the company, then it may make sense to speak to the district manager. But it should be out of concern for the company, not out of concern for how your manager is treating you as an employee (unless, of course, it should become a matter of work-related abuse in which case you would certainly be justified in going over your manager's head.)
I see this is your first post here on PC. So... welcome to PsychCentral!

I hope you find the time you spend here to be of benefit.
I don't know, of course, if you're here simply seeking advice with regard to this particular concern or if you plan to hang in here with us.

However, should you be planning to continue on (we hope you do)... may I suggest you introduce yourself over on PC's New Member Introductions forum? Here's a link:
https://forums.psychcentral.com/new-...introductions/
There's a lot of support that can be available here on PC. The more you post, & reply to other members' posts, the more a part of the community you will become.

Plus there are the chat rooms where you'll be able to interact with other PC members in real time (once your first 5 posts have been reviewed & approved.) So please keep posting!