I believe people do have more religious free with tenants of anti-clericalism. Having an anti-clerical mindset allows, Christians especially, to dissect the religion in the way the see fit or in ways that may make more sense to them without feeling the need to coincide with how others see it.
When a clerical society takes over, religion tends to become dogmatic and those who disagree are either shunned or punished in another way. But without too much clerical interference, the structure is free to grow and change and spirituality takes more precedence instead of dogmatism. The institution is seen for what it is, another power structure of society.
Clergy are the leaders of churches. They guide followers in pursuing lifestyles that are consistent with religious teachings and act as a sort of authoritative figure within the church. Once clerics are removed, the authoritative guiding figure is gone, and people are free to pursue religion as it pertains to them on an individual level. In that regard, anti-clericalism does promote more religious freedom.
Maybe people do have enough freedom to exercise their religious views in some parts of the world and so to with tenets of anti-clericalism and maybe even more so with the latter. It probably has much to do with which country they are in that will determine exactly how much freedom they will have.
Anti-clericalism is a historical movement that opposes the clergy and I believe this movement does give people more religious freedom, but I think it makes them more likely to drop their religion all together. I think anti-clericalism can be the start of people moving to a different faith or possibly just becoming more spiritual.