The SNP party leader’s intervention appears to have been prompted by unpleasant exchanges on social media following Scotland’s defeat in the Rugby World Cup.
A ‘Wings Over Scotland’ twitter account questioned the right of author JK Rowling to support the Scotland team because she helped fund the pro-Union Better Together campaign.
This is not the first time Ms Sturgeon has spoken on the subject via social networking.
She has previously tweeted in support of journalists and political opponents who have been attacked on social media.
At the weekend, in her speech to the SNP conference in Aberdeen she said her party “will respect those whose opinion differs from ours”.