There are griefing objects that can be rezzed on a region; anyone who goes there will have their HUDs and all other scripted attachments put into a non-running state. For instance: a HUD for a mesh body, and all the mesh body parts you are wearing, may be broken at the same time.
You might also have been affected by what appears to be a server-side bug: BUG-41379.
Below are things you can try to get the HUDs working again. First of all, relog then test the HUD(s) again. That may be enough. If not, read on.
Things to try:
Stay in a script-enabled region to do all of the following:
Inventory, right-click the item → Edit, and while it is in Edit, go to
Build menu → Scripts → Reset Scripts, or
Build menu → Scripts→ Set Scripts to Running).
Inventory > Current Outfit folder, and see if you are wearing any HUDs you were not aware of. (Note: HUDS do not necessarily have “HUD” in the name.) This could include temporary “Experience” HUDS that you may not be aware were attached.2)
Inventory → Right-click → Detach from Yourself, then
Inventory → Right-click → Attach to HUD, and choose an unused point.