The poll also found the decision to sack the high-profile MP was twice as likely to be backed by SNP voters than not.
Savanta ComRes, for The Scotsman, interviewed 1,002 adults aged 16 or over online between February 4 and 9.
Almost 40 per cent (37 per cent) of Scots backed the general principle of GRA reform, the poll found, with just over one in four (26 per cent) opposing the moves by the SNP to bring in rules allowing transgender people to self-identify as the gender of their choice.
A further 27 per cent said they had no opinion, with 10 per cent stating they did not know.
There is also a stark generational divide on the issue, with those aged under 55 more likely to back reforms than oppose them and 59 per cent of those aged 16-24 backing the plans.
This is contrasted with 44 per cent of those over 55 who are opposed to the proposals.
Women are also more likely to back the plans than men despite concerns over the impact the proposals could have on single-sex spaces.
A total of 44 per cent of women support the reform versus 16 per cent who don’t. A further 27 per cent said they had no opinion and 12 per cent said they didn’t know.
Men were more likely to oppose the plans, with 35 per cent disagreeing with the plans, 29 per cent supporting them, 28 per cent holding no opinion and 8 per cent saying they didn’t know.
The figures come as SNP voters are shown to be twice as likely to back the sacking of Ms Cherry (32 per cent) than oppose it (13 per cent).
Those most opposed to the move appear to be Scottish Conservative voters and older Scots aged over 55, with 30 per cent and 31 per cent respectively opposing the decision to strip the MP of her frontbench position.
Most people responding to the survey across all categories either responded don’t know or said they had no opinion, suggesting the incident has not cut through to the majority of voters.
Chris Hopkins, associate director at Savanta ComRes, said it was further evidence of Nicola Sturgeon’s strong position within the SNP.
He said: “Support for the proposed changes to gender recognition laws in Scotland are unsurprisingly driven by the young, Labour and SNP supporters, although a fair chunk of the population as a whole (27 per cent) neither support nor oppose the issue, implying that it’s salience among voters is fairly low and therefore changes – or lack of change – to the law is unlikely to shift voters.
"And further, while many Scots don’t have a view either way on Joanna Cherry’s sacking – 57 per cent neither support nor oppose the decision, or do not know – supporters of her party are more than twice as likely to support her sacking than oppose it.
"Consistently, SNP supporters side with Sturgeon on matters that could divide the party, putting the current SNP leader in a continually strong position among voters and within her own party.”