New research for the Oasis Foundation has found 65 per cent of people are worried about the church getting involved in health care.
Many people cited concerns that equality wouldn't be respected with a quarter of people worried the LGBT community would face discrimination in Church run public services.
A further 37 per cent thought the Church could use its provision to try and convert people.
Founder and global leader of Oasis, Revd Steve Chalke, told Premier the organisation had recently taken over the running of a library in London from Lambeth Council.
He said: "They want to know, is this library going to be open and accessible to everyone.
"Will your book choice be dominated by your world view or will the books you have on your shelves allow for other people's world views and outlooks?
"I think it's a significant barrier to the Church being involved at a great level of community engagement until we think through some of the wider issues of the acceptance of all people."
Oasis Church runs a school in Lambeth which has been rated outstanding by Ofsted, but despite that 55 per cent of those asked in the survey did not want to see the Church take a bigger role in education.
There was more confidence in the Church running foodbanks, youth groups and debt advice with 65 per cent happy for faith to play a part in the services.
"If the Church is to truly embrace this opportunity and deliver more complex public services on a national scale it still has a big job to do in managing perceptions and winning over the trust of the general public," Revd Chalke added.
The study also found a majority of churches were reluctant to take on public services, with most citing financial concerns and a lack of expertise.
Premier's Alex Williams speaking to Revd Steve Chalke: