He claimed the publicly-funded NHS was discriminating against lesbians and gays in their fight to secure services such as IVF treatment and sperm donation.
Peter Tatchell, of Outrage!, said the vote at the society's annual conference in Belfast represented a signficant breakthrough in the fight to make IVF techniques available to same sex couples.
BFS chairman Dr John Mills welcomed the outcome of the vote, but warned that gay men may not receive public support for their campaign.
About two thirds of delegates backed the motion tabled by Mr Tatchell and Manchester-based consultant gynaecologist Dr Anthony Nysenbaum supporting the right to same sex parenting.
Equality
Mr Tatchell, spokesman for gay human rights group OutRage!, told more than 100 top medics and scientists his argument was based on equality for all sections of society and a responsibility to safeguard children's welfare.
He claimed the publicly-funded NHS was discriminating against lesbians and gays in their fight to secure services such as IVF treatment and sperm
donation.
He said: "The NHS is funded by taxation. Lesbians and gay men are taxpayers too and we have a rightful claim to the services we contribute towards providing.
"To require us to pay for services that we are denied is ethically indefensible."
He also argued the scale of planning involved in providing a child for gay couples through donor insemination and surrogacy methods often makes them better parents than their heterosexual counterparts.
And he quoted from a City University in London study to back claims that children of lesbian mothers suffer no disadvantage.
The research carried out by two professors over a 14-year period found only two of the 39 children studied grew up to be gay, he said.
Before Mr Tatchell put his case a preliminary vote on the motion found delegates split 50-50.
Insisting the swing proved the validity of his arguments Mr Tatchell added: "The vote clearly represents the views of doctors and scientists working in the field of human fertilisation.
"This is the popular vote by professionals in favour of same sex parenting."
Not representative
He said: "This was a debate to stimulate discussion and early thinking in a process.
"Nothing has changed but in general terms we should be cautious of ruling out treatment for any groups on the basis of sexuality as well as race, religion and other social factors."
Dr Mills said a gay male couple would require much greater IVF surrogacy technology.
"I do not feel that there is a mood in this country to support this at this time.
"It's likely that more lesbian couples might seek to have a child and I think the vote carried out today perhaps represents support for these same sex couples rather than two men."