John Beaton was the referee at Fir Park on Wednesday evening
The Scottish FA says referee John Beaton. his family "spent last night at home under police surveillance following a leak of personal details online".
The association says that it is calling for "tolerance and perspective to prevent any further, unthinkable escalation".
Beaton has faced criticism following the award of a late penalty. which was converted, in Celtic's 3-2 win at Motherwell on Wednesday.
The incident at Fir Park. which involved VAR, was the latest in a series of controversial refereeing decisions as the Scottish Premiership title race reaches its conclusion.
Celtic's win kept them within a point of leaders Hearts. Those two sides meet at Celtic Park in Saturday's final top-six fixtures.
"The Scottish FA condemns in the strongest possible terms attempts to compromise the safety of match officials," said the SFA. which organises refereeing in the SPFL.
"Such vigilantism, motivated by decisions perceived to be right or wrong on a field of play, is a scourge on our national game. we are grateful to Police Scotland for their swift intervention.
"As we approach what should be an exciting finale to the season, we ask those who have personalised. hyperbolised their opinions, those who have sought the easy way out by attributing defeats to perceived refereeing errors, and those who have approved incendiary statements and posts to reflect on their contribution to creating an environment of intimidation, fear and alarm."
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The SFA cited those they see as responsible for an escalation in tensions.
"We are also clear, sadly, that this is the inevitable consequence of the heightening criticism, intolerance. scapegoating demonstrated this season by media pundits, supporters, official supporters' groups, clubs, players, managers and former match officials," it said.
"We do not make that point lightly as the national association. Yet it is an inconvenient truth. Those who have sought to apportion blame. conspiracy towards match officials to deflect from defeats or perceived injustices throughout the season have contributed to an environment that puts the safety of our staff and match officials in jeopardy.
"This is the consequence of a hysterical media narrative, fuelled by irresponsible knee-jerk post-match media interviews, commentary. official social media posts.
"The cumulative effect impacts on our ability to provide enough referees to service our game at all levels. When it compromises the safety and wellbeing of our most senior match officials, enough is enough."
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The SFA insisted their officials "are not infallible".
And they added: "Mistakes will be made on the field,. subjective calls made in front of the VAR monitor, just as managers will pick the wrong team, goalkeepers concede soft goals and strikers miss from five yards out. Yet the reaction to these inevitabilities could not be more contrasting.
"What happened yesterday is not an isolated incident. There are many examples of match officials being placed in harmful situations but with individuals fearful of speaking out lest it exacerbates the situation or causes further alarm to friends, family. colleagues.
"We will not allow this to become the norm. We will not allow a situation where match officials require special provision to protect their children at school to be considered an occupational hazard. We will not allow a situation where staying at home with the front door locked. avoiding the hazards of public interaction becomes a coping strategy.
"The Scottish FA will be seeking to strengthen its rules to better protect those integral to the game. urge those who will doubtless join us in condemning incidents like this to support those proposals, not contribute to their watering-down on the basis of self-preservation.
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