According to the accusations, the number of days the Union flag is displayed will be cut from 15 to just one - Remembrance Day.
The row comes amid claims published guidance has been changed for 2018.
Critics say the Union flag has been previously flown above many of Scotland’s best-known public buildings and visitor attractions - but the Scottish Government said there had been no change in policy since 2010.
First Minister Nicola Sturgeon described the criticism as “nonsense”.
Taking to Twitter, she said: “It has been the practice to fly the Lion Rampant from government buildings on Royal occasions since 2010.
“There has been no change in policy or practice since then.”
The Scottish Government said the published guidance had been updated by officials to reflect actual practice since 2010 and the Union flag will be flown on the same number of days in 2018 as previous years.
However, Theresa May’s official spokesman said it was up to the SNP Government to explain why the Union flag was no longer being flown on important public dates such as the Queen’s Birthday.
“It’s up to Nicola Sturgeon and the Scottish Executive to explain the reasons behind their decision,” the spokesman said.
“The Prime Minister thinks [the Union flag] is an important symbol of our Union, and the Union is something that she believes in fiercely.”
A spokesman for Labour leader Jeremy Corbyn refused to be drawn on the row, saying it was “entirely a matter for the Scottish Government”.
SNP Westminster leader Ian Blackford also played down the dispute, saying: “There is no issue about any disrespect to any flag in any of this. It’s about respecting the Royal Family, if anything, and about respecting the important anniversaries that we have to mark.”
Asked if Scots “give two hoots” about which flag is flown, Mr Blackford added: “No, in short.”
The Ross, Skye and Lochaber MP said opposition leaders at Holyrood said: “We have to recognise that there are divisions in society, and the responsibility that all of us have is trying to heal those divisions as far as we possibly can.
“We have to understand that there are different opinions on these things and be respectful. That responsibility extends to the other opposition leaders as well, and not to try and trumpet these things as something which they are not.”
Conservative MSP Murdo Fraser said: “Nicola Sturgeon is always keen to stress that her civic nationalism is nothing to do with flags and banners. Yet here we have her trying to eradicate the Union flag from government buildings in Scotland.
“This is another example of the SNP pushing its separatist agenda by stealth.”
He added: “Refusing to fly the flag on the Queen’s birthday may well appeal to the extreme elements of the nationalist movement, but ordinary members of the public will be altogether less convinced.”
A Scottish Government spokeswoman said: “There has been no recent change whatsoever to the policy or practice relating to the flags that are flown from government buildings.
“The Royal Banner (Lion Rampant) has been flown on Royal occasions since 2010.
“The policy has not been changed under the current First Minister - the public guidance has simply been updated by officials in response to queries to match long-standing practice.”
Former First Minister Alex Salmond has also waded in, claiming responsibility for the change he claims took place in 2010.
He said: “The hoisting of Lion Rampant had nothing whatsoever to do with Nicola Sturgeon.
“I changed the policy on flag flying back in 2010 after an audience with Her Majesty the Queen at Balmoral the previous year.”
Leader of the Scottish Conservatives, Ruth Davidson, labelled the changes as “dismal stuff”.
She added: “The SNP government should be more concerned with raising standards, not lowering flags.”
But Ms Sturgeon hit back at Ms Davidson, tweeting: “Memo to PM’s new ‘fake news’ unit. The first line of defence against fake news is for your own politicians to stop peddling it.”