The tweet was sent from the force's official Twitter account on Monday, September 10 and has since been retweeted and commented on hundreds of times on the social media account.
Comparisons were made by some with author George Orwell's dystopian novel 1984, in which the state is ruled by an omnipresent government, while others were outraged that police were putting resources promoting this.
The tweet read: "Hate can cause a range of emotional responses, including fear, anger and shock.
"People experience mental and physical well-being issues such as problems sleeping, depression, anxiety and paranoia.
"Hate hurts and no-one should have to tolerate it #HateHurtsSY"
Oliver Hopkins-Burke replied: "Hate may be unpleasant, but it is not a crime. It’s not your job to stop people from engaging in non-criminal activity.
"Furthermore, you do not decide what is illegal, legislation does."
Jonathan Trotter said: "In case no-one told you the novel 1984 was a warning not an instruction manual.
"You cannot make a crime out of something because someone has their feeling hurt! #noliberty"
Sergei Epatov said: "Orwellian 1984's Thought Police."
Ray Norshine said: "Which number do the crybabies call if they feel slighted?"
National radio presenter Nick Ferrari and other media outlets, such as The Times and the Evening Standard have also picked up on the tweet.
South Yorkshire Police responded with a statement on their website saying that they were not encouraging people to report eveything that offended them, but that the social media post in relation to an incident over the previous weekend.
Chief Constable Stephen Watson said: “There has been much speculation and discussion in traditional media and across digital platforms about our Hate Crime policy.
“This discussion began following an incident in Barnsley town centre last weekend, where a man was stabbed. Legal proceedings are now ongoing in relation to this matter and therefore it is not appropriate or lawful to provide further comment at this time.
“This incident and the statements issued on our force social media accounts provoked a wave of social commentary which was racist, abusive and offensive.
“In the face of some pretty outrageous comments we felt compelled to reassure our communities that we do not share the views of those individuals using social media to voice their hatred, and to remind everyone of hate crime and its impact on those affected.
“This appears to have been deliberately misconstrued and manipulated by some media outlets and individuals on social media to misleadingly suggest that we are encouraging people to report any incident that causes insult. This is not the case. Social commentary about drivers cutting up one another on roads, or people being insulted due to opposing views at a football game, is misleading and incredibly unhelpful.
“We encourage reporting of hate incidents much the same as we encourage victims of domestic abuse to report incidents to us, or communities feeling beset by antisocial behaviour to report incidents to us. Not all of those incidents reported to us are crimes, nor will they receive a police response, but it gives us (and our partner agencies) a good indication of what’s happening in our communities and directs our preventative, proactive police work to try and stop crimes from happening in the first place.
“I am sure victims of domestic abuse and communities experiencing antisocial behaviour are reassured by the fact they can call us about any incident, knowing that we’re there to support and listen. Why should victims of hate receive a different service or have a different expectation of our force?
“Our approach throughout our Hate Hurts campaign, which has been running for over a year now, has always been to reach out to vulnerable individuals and communities who are subject to abuse and persecution based on their race, religion, gender identity, sexual orientation or disability.
“We do this to better understand issues of hatred within our communities and to prevent such abuse manifesting itself in the way it did with the death of Fiona Pilkington.
“Had this issue not been so misrepresented, I doubt that we would find ourselves having to defend the policing approach to such an important issue. Keeping people safe is a key facet of what police officers do across the UK and a key element of our many responsibilities is to protect and support vulnerable people in our communities.
“Our policy is no different to any other force in the country and is a national initiative to ensure that any individual who feels persecuted or targeted by hate has trust and confidence in their police.
“The deliberate misrepresentation of our approach has created an unhelpful distraction.”