Heterosexual politicians calling for a plebiscite on same-sex marriage don’t understand the fear and animosity faced by LGBTI Australians, the senior Labor frontbencher Penny Wong has argued.

Wong made the remarks in the Lionel Murphy memorial lecture at the Australian National University on Tuesday.

For gay and lesbian Australians hate speech is not abstract Penny Wong

She raised the fact that LGBTI Australians face abuse online, that they are still victims of assault and fear holding hands in public, to demonstrate their opposition to a divisive plebiscite is well-founded.

It comes after the prime minister, Malcolm Turnbull, said on FM radio in the Northern Territory on Tuesday that Bill Shorten was “running a scare campaign about a plebiscite on gay marriage”. Turnbull said a plebiscite would be conducted in a civil and respectful way.

“Bill Shorten should have more respect for the decency and common sense of Australians,” he said.

Labor has stepped up its attack on the government’s plan for a plebiscite on the issue, Shorten describing it on Sunday as “a taxpayer-funded platform for homophobia”.

In the lecture, Wong said the non-binding plebiscite was “just the latest in a series of obstacles erected by opponents of marriage equality”.

The senator said the former prime minister Tony Abbott had proposed a plebiscite “because he had exhausted other avenues to stymie the demand for a free vote in the Liberal party room”.

Wong said Turnbull’s claims the plebiscite campaign would be respectful were “the hollowest of hollow words”.

“I know that a plebiscite designed to deny me and many other Australians a marriage certificate will instead license hate speech to those who need little encouragement.”

“Mr Turnbull – and many commentators on this subject – don’t understand that for gay and lesbian Australians hate speech is not abstract,” Wong said.

She said she faced abuse in her Twitter feed that signalled “words that hurt” would be used in the debate against LGBTI Australians less resilient than herself.

Wong said assaults – and worse – of LGBTI Australians were not unknown, even today. “Many gay and lesbian people don’t hold hands on the street because they don’t know what reaction they’ll get,” she said. “Some hide who they are for fear of the consequences at home, at work and at school.

“Not one straight politician advocating a plebiscite on marriage equality knows what that’s like. What it’s like to live with the casual and deliberate prejudice that some still harbour.”

Wong argued Australia did not hold plebiscites on other fundamental issues of justice and human rights, such as abolishing the death penalty, ending the white Australia policy or enacting the native title regime.

“I don’t oppose a plebiscite because I doubt the good sense of the Australian people. I oppose a plebiscite because I don’t want my relationship – my family – to be the subject of inquiry, of censure, of condemnation, by others.”

The Greens’ LGBTI spokesman, Robert Simms, told Guardian Australia he was worried about the effect of the plebiscite on young people.

“I remember my own process [of] coming out. How in my home state of South Australia at the opening of the gay lesbian pride parade there were street preachers [railing against homosexuality],” he said. “I would hate to imagine the effect we’d see in a national plebiscite.”

Australian Marriage Equality has renewed its calls for same-sex marriage to be legislated by parliament, with a campaign in the federal election opposing the plebiscite.

Wong’s speech comes as the Australian Christian Lobby released an election guide blasting Labor for opposing a plebiscite. It also claimed Labor’s policies to recognise transgender people’s gender identity would “make public toilets unsafe for women and girls”.

AME national spokeswoman Shirleene Robinson told Guardian Australia: “Everyone is entitled to their views but we must remember we are talking about real people, members of our families, our friends and neighbours and our tone and and language must respect their dignity.

“Words can inflict terrible harm sometimes and we would ask that people of all opinions remember that. Our Australian values are based on a fair go and respect for all and its important that these values underpin our national conversation on marriage equality.”

Debate in Australia has been marked by controversial material against marriage equality, including a pamphlet printed by a former MP claiming children of same-sex couples may be more likely to be victims of sexual abuse or abuse drugs, and a booklet sent to Catholic schools warning that “same-sex friendships” are very different from “real marriages”.