Shifter mode will not change to manual when using the shift up or down buttons

Yes, this was a deliberate choice. Most new users were accidentaly shifting and enabling manual transmission, which resulted in frustration. Not fun. Just hit the Q key.

Note that your preferred shifting mode is remembered by the game since last update, so you only need to do it once, and all new vehicles you spawn from that point on will use the same mode when available (or a different one when the car is not fitted with the appropriate transmission parts).