US Style Freedom of Religion

It's not unreasonable to adduce that faith leaders in the US have more social influence than does the government. This is in contrast with China, where, although there is enormous freedom of religious practice, faith institutions do not have more power over social and political outcomes than the CPC.

Multicultural and multifaith cultural and social dynamics - especially the existence of large mutually ideologically opposed religious communities - are probably all that stops effective full fledged autocratic theocracy in the US.

It is unlikely that the secular defenders of the US constitution would be able to resist and repel a strong religiously homogenous majority from usurping and overturning secular and ecumenical conventions in the US. This is because the largest religious groups, such as Catholicism and Evangelical Protestantism are broadly dominionist: they believe that their religious tenets and religio-cultural imperatives should apply to all individuals in all human societies.

This threat does not exist for the CPC. Many influential religions in China, such as Daoism and Buddhism are naturalistic (not supernaturalist) and are neither overtly, nor even nominally, dominionist.

A similar situation to that in the US exists in Australia: a British Commonwealth member nation. However, this is more due to incidental religious demographics than to any constitutional imperatives. Australian demographics are split roughly three ways between Protestant Christian evangelicals, Catholics, and other religions and non-religious groups. If the Protestant and Catholic populations became religiously and ideologically homogenous (an unlikely outcome) then it is unlikely that secular imperatives would have any significant influence in Australia.

Recent demographic and census data indicating that non-religious groups make up approximately 40% of the population may be misleading. Several Protestant Christian sects and denominations have Christian anarchist ideologies, and, given no other choice, their adherents will often identify themselves as non-religious. They will express a commitment to a belief in a distinction between faith and religion. This is in part influenced by anti-Papist sentiments, and opposition to state religion, similar to that expressed by early European Puritan settlers in the Americas. It's interesting to note that in-principle opposition to state religion does not seem to preclude commitments to dominionist imperatives on the part of many large evangelical sects.