Reverend George Gebauer told Aimi and Victoria Leggett that they could not both be registered as one-year-old Alfie's mothers.
Instead, the Church of England clergyman suggested that one of them should be listed as godmother because the baptism certificate only has space for one mother and one father.
The 87-year-old from St Mary's Church in Warsash, Hampshire, told them it was 'impossible' for Alfie to have two mothers and refused to conduct the ceremony claiming it could be 'illegal' to proceed in the way they wanted.
The couple, who married in a civil ceremony, were so upset that they stormed out of the meeting with the vicar.
Alfie's birth mother Aimi, 25, said: "There was no way one of us was going to be listed as the godparent. We are both Alfie's mum.
"Rev Gebauer sat there and told us no child could have parents of the same sex, no child could have two mothers.
"He did this for about 10 or 15 minutes and was asking us why we want Alfie brought into the church."
She added: "I'm baptised Church of England and Victoria is a Catholic. We want him to be brought up Christian, the same that we have been.
"We were even saying to the Reverend: 'Do you want Alfie to be ashamed of his family?' He's not gay, we are, what we do is up to us."
Full-time mother Aimi and law student Victoria, 22, who live in the nearby town of Fareham, had initially organised the baptism with Rev Andy Norris – who has since moved away from the church. Retired vicars, including Rev Gebauer, are now officiating until a replacement can be found.
But the vicar claimed the couple's sexuality was not an issue and that he had been willing to baptise Alfie if they agreed to record just one of them as mother.
He added: "They insisted they both be registered as mum and refused to budge from their position. They will not give way and that can't happen. Their sexuality has no bearing on the issue. It was never discussed. The church baptism register makes no provision for it.
"We have bent over backwards to try and accommodate this family. I believe it would be illegal for me to register them both as mother."
With tensions high, the Archdeacon of the Meon, the Ven Gavin Collins, has now intervened in the row. He said the christening can go ahead without Rev Gebauer – with both women named as mother on the certificate.
He said: "Having spoken to Aimi Leggett, I'm pleased to report that the baptism of Alfie will go ahead at St Mary's Church.
"We have addressed the legal issue. As I understand it, her partner Victoria has full legal co-parental responsibility for Alfie.
"We will therefore be able to enter their details on to the baptism register as mother and mother, as they would like.
"I'm pleased that this issue has been resolved, and we are looking forward to welcoming Aimi, Victoria and Alfie, as well as their friends and family."
Aimi's mother, Donna Leggett, 44, said: "Somebody from the church phoned to say sorry and to say the baptism can go ahead. It's great news but it should never have got to this stage in the first place."