"Time and time again" the pontiff had shown prejudice against gay and transgender people, the group claimed in a series of tweets to its 63 thousand followers.
It was responding to reports that Pope Francis had said allowing children to choose their own gender was against God's will.
In a transcript by the Vatican released on Tuesday the Pope said: "God created man and woman, God created the world this way, and we are doing the opposite."
The BHA appeared to link the Pope's Biblical beliefs with reports of child abuse, saying: "Obviously the Catholic Church has form when it comes to denying 1) children's accounts of their experiences and 2) scientific consensus."
Another tweet read: "To deny decades of scientific research and instead dehumanise trans people all over the world like this just takes the cake. Just awful.
"We hope one day the world will stop looking to men in hats interpreting myths for moral guidance on issues best left to science & philosophy."
The final tweet on the issue said: "The Pope has shown time and time again that he is profoundly homophobic and transphobic. When will people stop revering him as a progressive?"
Pope Francis has been credited with showing a more compassionate attitude towards gay people since taking the role.
He has repeatedly said gay people should not be marginalised but instead welcomed into the Church.
"If a person is gay and seeks God and has good will, who am I to judge?" He famously said in the early stages of his papacy.
Earlier this year he took the extraordinary step of calling on the Roman Catholic Church to apologise to gay people for the way they have been treated by Christians.
The Church had no right to judge gay people, he said.
During a press conference he said: "I will repeat what the catechism of the Church says, that they [homosexuals] should not be discriminated against, that they should be respected, accompanied pastorally."
The British Humanist Association did not respond to a request for comment.