Mackay is expected to be unveiled in the job despite previous allegations that he exchanged racist and sexist text messages.
The allegations surfaced after Mackay was sacked by Cardiff City in 2013.
Show Racism the Red Card said Mackay had undergone equality and diversity training, and "wished him well".
And Lord Ouseley, the founder and chairman of the Kick It Out anti-racism group, said he believed Mackay now had a "better understanding" of diversity issues and deserved a second chance.
He also said Mackay's new role would give him an opportunity to "put himself back in a state where he can prove that he is a good person, and a person capable of performing both in football terms, and how he treats people".
But SNP MSP Clare Haughey called on the SFA to "see sense" and rule out Mackay as a candidate, arguing that his appointment would send out the wrong signals.
Mackay, a former Scotland and Celtic player, was the subject of an English FA investigation in 2014 concerning text messages he had sent containing discriminatory language.
He apologised for his actions and stated a desire to return to football.
The SFA is expected to unveil Mackay in the role of performance director on Thursday.
The post became vacant when former Manchester United striker Brian McClair quit in July.
In a statement issued to BBC Scotland, Show Racism the Red Card said: "After admitting to sending text messages that were very regrettable and disrespectful to other cultures, Malky Mackay underwent equality and diversity training through an education programme with the FA and we wish him well in his new role at the SFA."
After a lengthy investigation, the Football Association said last year that Mackay would face no action over the text messages, which it said had been sent with a "legitimate expectation of privacy".
But it said Mackay had been spoken to "about the inappropriateness of terms used in the messages"
Mr Mackay's agent, Raymond Sparkes, told BBC Scotland that the FA's investigative committee had examined 9,000 texts exchanged between Mackay and Cardiff City's former head of player recruitment Iain Moody.
Of these, three sent by Mackay were found to have been unacceptable - with Mackay immediately apologising.
Mr Sparkes added: "If you were to know Malky Mackay, you would know him as a good man, from a good family, with good values.
"He is a talented individual, he has had three years of not being able to take his place back in a place of employment on the back of three text messages.
"We know why that penalty has been placed upon us, we have dealt with it, we want to get back to work and we didn't just apologise now - we apologised then."
Ms Haughey, the SNP MSP for Rutherglen, told the BBC's Good Morning Scotland programme that Scottish football had made "huge efforts" to tackle racism and homophobia and to promote women's football.
And she said appointing Mackay would risk sending a message that inappropriate behaviour was "no barrier to a top job in Scottish football".
Ms Haughey added: "Young people look to football for role models, and one of the most important jobs in Scottish football is not the place for someone who felt these conversations were an acceptable part of football culture.
"The SFA really needs to see sense and rule out this appointment."
Paul Goodwin, of the Scottish Football Supporters' Association, told the same programme that many fans were surprised that Mackay had emerged as the front-runner for the job.
But he said there had to be some sort of balance, and pointed out that people who have done "worse things" than Mackay had successfully been rehabilitated back into the system.
Mr Goodwin added: "It is a really a very difficult place for him to be, and I would suggest at this moment in time a difficult place for the SFA to be too."
Anti-racism campaigners have backed the appointment of Malky Mackay as the Scottish Football Association's new performance director.