How can some manganese oxides be acidic and some basic?
This is not a property only for manganese but also for other elements like Chrome, Bismuth and other "amphoteric" elements. The phenomenon is due to the inductive effect of the several oxygen atoms that are present in the molecule at high value of potential. These oxigen atoms because of inductive effect attract electrons of the molecule leading to release hydrogen atoms (Lovry- Bronsted theory), or show lone pair attractions (Lewis theory).
For the manganese you have MnO and its idroxide