Can anxiety or stress cause my butt to itch?

Not so likely: More likely you have a bug bite or some kind of skin reaction to soap or other product you're using. If you cannot see the area well by yourself, please ask a friend to look. If very severe, see your physician.

Yes: Yes and here's a mostly complete list of other causes: soaps, ointments, vitamin c supplements, beer (yes, beer!), caffeine, excessive sweating, antibiotics, diabetes, pinworms, scabies, candida (fungus), allergy (atopy), and bacterial infections from scratching. Good luck!