Mackay was dismissed by Cardiff City in December after falling out with owner Vincent Tan, and looked on the verge of taking over at Crystal Palace in August following Tony Pulis' departure from Selhurst Park.
That was until he was reported to the FA over text messages he exchanged with then Cardiff head of recruitment Iain Moody, which he admitted were "disrespectful of other cultures".
On Wednesday, Mackay was given another chance in management by Championship strugglers Wigan, who sacked Uwe Rosler earlier this month.
Subsequently, Kick It Out released a statement appearing to criticise the appointment, with Mackay thought to still be under investigation for his previous conduct.
"The Football Association began investigating in August alleged racist, antisemitic, sexist and homophobic comments made by Malky Mackay and Iain Moody, and we are still yet to hear whether this is near to reaching its conclusion almost three months on," the statement read.
"Where does the case now lie and how close are we to seeing whether the FA will take the appropriate action?
"Wigan Athletic have disregarded the ongoing investigation being undertaken by the FA, and any potential punishment Mackay may face, by taking the decision to appoint him.
"We need to see leadership, and a respect for the processes in place, shown by football club owners to demonstrate how seriously they take tackling issues of exclusion, prejudice and discrimination.
"It is essential high levels of conduct are maintained by those in positions of power such as club owners, boardroom officials, chief executives, managers, coaches and players, and we expect the FA, the Premier League, the Football League, the Professional Footballers' Association and the League Managers Association to ensure these standards are upheld at all times.
"It remains to be seen if Wigan's position is one which the FA and all of football's so-called 'family' are happy with.
"The FA now needs to move swiftly to let everybody know whether they agree with Wigan's position or whether they will reinforce their own zero-tolerance stance on all such matters of equality and diversity. We await the FA's response before commenting further."
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
