It's speaking as a consultation over the government's Counter Extremist Strategy continues, where Christians and others can submit evidence and have their say.
Under the current recommendations Ofsted inspectors would regularly visit children's places of education outside of schools to ensure they aren't being radicalised, if the children attend those places for more than six hours a week.
The EA has said that church activities including youth clubs, Bible studies, Sunday schools and festivals could be included in the out-of-school activities monitored by Ofsted, and that this could become the state monitoring and interfering in what the Church does.
Simon McCrossan, Head of Public Policy at the EA, told Premier: "The proposals are potentially so wide that they would capture the registration, inspection and regulation of large swathes of church life.
"Whether it is intentional or not by the government... this could amount to the indirect state regulation of private religious practice, and that's not a feature we're used to in a free, liberal democracy.
"They [Ofsted] do of course reserve the right to identify unsuitable teachers and undesirable teaching. Well of course that raises the question 'how does one decide what that is?' And there's a real concern that historical, biblical doctrine might be interpreted as incongruous with ideas such as British values.
"The government has to secure and recognise our fundamental freedoms within their strategy to deal with extremism. We don't want to see the withdrawal of great supplementary education that Christians of all denominations do in some of the most vulnerable and challenging contexts."
A DfE spokesman said: "We recognise many out-of-school education settings do a great job in supporting children's education and development but, without proper oversight, there is a risk that some children attending them may be exposed to harm, including from extremism.
"We want to hear the views of all interested parties about how settings which children attend intensively might be required to register so that they can be inspected in a way that does not place unnecessary burdens on good providers.
"We will take all responses into account when considering the next steps."
The government's consultation on its Counter Extremism Strategy ends on 11 January 2016.
Listen to Premier's Aaron James speaking to Simon McCrossan here: