Ms Forbes, who was appointed public finance minister by Nicola Sturgeon 18 months ago, has been criticised by LGBT activists in her party claiming she has "questionable views" on equality because of her religious beliefs.
A member of her party's National Executive Committee, and the national co-convener of the Out4Indy group, Josh Mennie said the promotion of Ms Forbes - who is being tipped to formally replace Mr Mackay as Cabinet Secretary for the Economy - "was the last thing our party needs".
He went on to link to a letter Ms Forbes had sent with 14 other SNP politicians to The Scotsman last year, which called for the Scottish Government not to “rush” into legislation they claim could change the definition of what it means to be male and female.
The tweet provoked a furious online response from many SNP members, who had praised Ms Forbes for filling in for Mr Mackay at the last minute to deliver the budget last week, after he was forced to resign from government amid revelations he had bombarded a 16-year-old schoolboy with text messages.
SNP Islands Minister Paul Wheelhouse, waded into the row telling Mr Mennie: "You really should reflect long and hard on your disturbing tweet".
He added: "There should certainly be respect for other people's sincerely held views on sensitive matters such as equalities/rights and for talented women who are making a difference in a world where they still face way too much discrimination."
And James Dornan, SNP MSP tweeted: "I’m wondering if what would help is if we could get a kind of political photofit of what kind of person is suitable to represent the SNP in their eyes. If the intelligent, kind & astute @KateForbesMSP doesn’t fit into that photofit then I suspect it’s them that’s wrong, not her."
Mr Mennie has since deleted the tweet, however he went on to say: "The majority of people slinging abuse at me re my tweet raising concerns over Kate Forbes views on LGBTQ equality are the same people who would welcome the roll back of LGBTQ rights."
And in responding to a tweet he added: "I disagree with Kate on GRA and also recognise she did a good job with presenting the budget. I’m fearful having a politician as a government secretary who has hinted toward anti LGBTQ views in times when hate crimes are rising toward LGBTQ people. It’s scary."
Last night Mr Mennie told The Scotsman: “Kate Forbes is a respected politician in the SNP, though in times when LGBTQ+ hate crimes are rising in Scotland, we need to be able to question and scrutinise the views of senior politicians representing us without fear of backlash.”
Ms Forbes, who has represented the constituency of Skye, Lochaber and Badenoch, since 2016, is the latest female SNP politician to be drawn into a row over gender reform which is dividing the party.
Her fellow MSP Joan McAlpine and MP Joanna Cherry have been attacked for their views on sex and gender, as they believe the two should not be conflated, and that the Scottish Government should not introduce the idea of "self-identification" for transgender people who want to apply for a Gender Recognition Certificate.
The statement, which was also signed by four leading SNP councillors, said that “conflating sex with gender identification affects a wide range of policy and service delivery, including data collection, education, health and social care, justice and sport. New information about this topic is emerging all the time and deserves to be properly scrutinised”.
It added: "“Changing the definition of male and female is a matter of profound significance. It is not something we should rush.”