Have we changed your mind? See below for some final thoughts.
Materialism is a thesis about the composition of things, whereas physicalism is a thesis about the relation between instances of properties. Materialism and physicalism are different. Externalists can be non-reductive materialists, but they are not physicalists.
Versions of biological naturalism (such as the naturalistic theories of mental content advocated by Fred Dretske, Ruth Millikan and David Papineau) are externalist and hence not physicalist theories.
Externalism applies not only to mental states such as beliefs, desires, fears, hopes, intentions, and so on, but also to actions. Just as one brain state can constitute any number of different thoughts (a thought about water, a thought about t-water, and so on), the very same physical movement (a certain wave of the arm, for example) can be any number of different actions (the hailing of a taxi, the greeting of a friend, the insulting of an enemy, and so on).
The problem of mental causation looks rather different if you’re an externalist as well. If mental states are not identical to brain states, and actions are not identical to bodily movements, then perhaps brain states can cause bodily movements, mental states can cause actions, and there be no competition between the two.