A Facebook post targeting the sexuality of Australian Greens leader Bob Brown demonstrates the need for tough anti-discrimination laws, a prominent gay rights activist has said.

On Thursday, the ABC revealed former Australian Greens leader Bob Brown had referred the post to the anti-discrimination commissioner, saying it was a homophobic slur.

The post was a historic photo of Mr Brown being dragged away from a protest by forestry workers in 1986.

It was captioned: "We have no idea why Bob would want to be surrounded by sweaty, hairy men", and included a crude comment implying Mr Brown's sexuality was a motivating factor in the protest.

The page's administrator, Brett Lucas, denied it was homophobic and said it was "humorous".

Gay rights campaigner Rodney Croome said the post was unacceptable.

"Life is already tough enough for young LGBTI Tasmanians without seeing a prominent Tasmanian mocked and vilified because he is gay," he said.

Bob Brown has taken his complaint to Tasmania's Anti-Discrimination Commissioner. ( ABC News: Scott Ross )

"The homophobic abuse directed at Bob Brown shows why the State Government is making a terrible mistake by weakening Tasmania's world-class hate speech laws."

The Tasmanian Government's plan to change the state's anti-discrimination laws have cleared the Lower House and are set to be debated by the Upper House later this year.

The changes would exempt religious groups from some provisions of the Act.

Marriage equality plebiscite 'a bad idea'

Mr Croome said posts like the one targeting Mr Brown would face less legal opposition if the changes went ahead.

"The State Government's proposal to water down Tasmania's hate speech laws will foster hate speech in the community, because it sends the message that there are circumstances under which hate speech is acceptable," he said.

Mr Croome said the case was "timely reminder of why it was such a bad idea to have a marriage equality plebiscite".

"The plebiscite would have given anti-gay hate speech the biggest platform ever," he said.

A spokesman for the Government rejected Mr Croome's claims.

"The Government's proposed changes relate to religious purposes only, and Mr Croome's claims are incorrect," he said.