Media attention on the June 23 vote could distract from the debate surrounding government plans to allow inspections at church Sunday schools.
Proposals would mean non-school settings caring for children for more than six hours a week could face Ofsted inspections.
The government says it is to clamp down on 'undesirable teaching' but critics warn traditional Biblical teaching could come under that banner.
Colin Hart, Director of The Christian Institute said: "The upcoming referendum on the UK's membership of the EU is on many people's minds right now. Clearly this is a profoundly important issue for the future of our country and it is right that as many people participate as possible.
"But Christians must not stop holding the Westminster Government to account over its proposals for Ofsted 'British values' inspections of church youth work, and Extremism Disruption Orders.
"Together these represent an attack on religious freedom and freedom of speech that we have not seen in this country since the days of John Bunyan, more than 300 years ago.
"I am very concerned that Government Departments could try to slip through highly contentious legislation which harms Christian freedoms while the media focus so heavily on the EU referendum.
"We will be on our guard but Christians across the nation also need to be vigilant and ready to speak out to prevent this happening."
An Ofsted spokesman said: "Ofsted has absolutely no intention of intervening in Sunday school teaching.
"Ofsted will act according to whatever criteria are set down by Parliament once any legislation that follows this consultation exercise is enacted.
"We have no current powers to inspect these type of settings unless we have cause to believe they are operating illegally as unregistered schools. Nor are we seeking any additional powers other than those that Parliament may decide to give us."
