The ruling party has been hit by divisions over reforming the Gender Recognition Act, with some high-profile figures expressing concern about women’s safety.
The Gender Recognition Reform (Scotland) Bill was introduced earlier this year, pledging to reduce the time a person has to live in their acquired gender from two years to three months, with a further three-month “reflection period” before they can receive a gender recognition certificate, as well as lowering the age at which one can be obtained from 18 to 16.
It is not yet known if SNP MSPs will be given a free vote on the issue as the Bill makes its way through Holyrood.
Speaking on BBC Radio Scotland, Green co-leader – and Scottish Government minister by virtue of a powersharing agreement between the two parties – Mr Harvie said the legislation would likely pass and “the sky would not fall in”.
He added: “I think it’s true that there is still a significant number of high-profile people within the SNP who have been allowed to get away with promoting transphobia.
“Some of the comments that I’ve seen online have been appalling.
“All political parties that I’ve seen have difficult processes when they try to reform their internal disciplinary processes – I can recognise that, it’s not always easy for any political party to deal with those kind of things, but it has been allowed to fester.”
He did not name those within the SNP he was referring to.
He added: “I think now we’re at a point where that’s a lot less of a problem now than it was a few years ago and it is pretty clear there is an overwhelming majority within the Scottish Parliament to proceed with this legislation, to do it in a calm and measured way, to answer questions and concerns that people have because those answers do exist and have been gone into thoroughly.”
Mr Harvie went on to say that if there is to be a “respectful debate” around the Bill, that discussion must be free of “transphobic prejudice”.
The Glasgow MSP concluded: “We’ll move on, and we’ll pass this legislation as other countries have and the sky will not fall in.”
An SNP spokesperson said: “The SNP is proud to be taking forward legislation to improve the lives of trans and non-binary people.”