Anti-clericalism is a historical movement that opposes the clergy for reasons including their actual or alleged power and influence in all aspects of public and political life and their involvement in the everyday life of the citizen, their privileges, or their enforcement of orthodoxy, according to Wikipedia. I believe that it has become mainstream in Christianity, at least within the United States. There are a lot of people here that uphold Christian values, yet don't attend church or listen to clergy at all. That's why you see a lot of people identify as "spiritual," but maybe not religious.
Although priests and ministers have historically been an important part of the Christian religion, they are not essential. The only requirement for Christians is that they accept Jesus Christ as their lord and savior. It is possible for Christians to be anti-clerical. In the future, this movement will likely gain more ground.
Wow, wouldn't that be nice if anti-clericalism could have some meaningful impact on modern Christianity in America? They're certainly corrupt and hypocritical enough so that any thinking churchgoer should have problems with it. However, it's unlikely to happen. Modern Christians aren't known for closely examining their articles of faith or questioning their churches.
Most mainstream Christian religions are essentially run by clergy. They tell members what to think, how to vote, how to behave and they do have a lot of power. I don't see this changing at any time. While there may be members of the clergy opposed to clericalism, I would guess they are in the minority. Organized clerics are too powerful.
Most members of Christian congregations go to that particular church because they like the minister and his or her message every Sunday. However, criticism of ministers is a pretty normal occupation for them. That is not going to change. Where it is warranted is when the cleric is arrogant or hypocritical as in some of the fundamentalist churches.