Jim Cullen, chief executive of the charity, which has renamed itself Caritas Care, said comments by Bishop of Lancaster Patrick O'Donoghue about same-sex adoption was 'a significant drive' behind the changes.
The Bishop said it would be 'unthinkable, indeed heart-breaking' for the agency to agree to new equality laws which came in last month, meaning it must treat gay and lesbian couples the same as heterosexual couples when it comes to finding homes for children.
Mr Cullen said: 'Bishop Patrick did say if we did comply with the law, we would not be able to call ourselves Catholic.
'We are still a Catholic charity in as much as everything we do is still driven by the teachings of the church, but we no longer receive support from the Diocese, in the sense it no longer provides any funding.
'We would have had collections to support us financially from the Diocese and receive other guidance from it, but that has now stopped.'
Bishop O'Donoghue stepped down from the charity's board of trustees at the end of last year.
Mr Cullen said the charity, which is based in Tulketh Road in Ashton, Preston, would feel the hit of losing the financial support as trust funds and councils which support it also feel the squeeze of the recession.
He said that it had not yet felt the impact of the downturn on councils it works for, but expected to in the near future.
The chief executive said: 'If these things conspire against us it will be very difficult. We will need to more than ever be tight and in control of our resources.'
Bishop O'Donoghue has declined to comment but in an open letter to the charity's trustees last October he urged them not to 'capitulate' to the changes in the law.
He said: 'I remain convinced the best interests of children are served when they live with and are brought up by a married couple.' [Lancashire Evening Post]