It's an interesting anecdote that of Arnold Schwarzenegger. There are some nuances though as to the kind of alleged economic freedom promoted by Republicanism and some restrictions in other areas. In Schwarzenegger's context it made sense; similar discourses are circulating now about how Latin Americans in the States should be Republicans because Democrats represent whatever issues made them run from their countries.
The fact of the matter is that there is no much of a difference between the two parties. The USA has advanced and sunk and recovered regardless of who is in office. In general, both parties carry out similar agendas when it comes to economic prosperity regardless of third parties involvement (meaning the rest of the world).
Obviously, and as a Venezuelan i can attest to that, state control is wrong, negative and detrimental to both the individual and the country as a whole.