Anti-Clericalism
Anti-Clericalism is defined by opposing clericals and the societal influence of organized religion in both governmental and public affairs. This differs from being anti-religious since you can just oppose organized religion but not religious practices themselves, and not all anti-clericals are atheists.
Anti-clericalism has been practiced by both religious people and anti-religious people, such as during the protestant reformation during Europe or in state atheist countries like the USSR.