Wigan could cancel Malky Mackay's contract if their new boss is found guilty by an ongoing Football Association investigation.
The FA is looking into allegations Mackay sent "sexist, racist and homophobic" text messages during his time in charge of at Cardiff.
Anti-racism group Kick It Out accused Wigan of "disregarding the ongoing investigation" in appointing Mackay.
"It's in the contract," said Latics owner Dave Whelan. "We are protected."
Kick It Out says Wigan should have chosen someone else to replace Uwe Rosler, who was sacked on 13 November.
In a statement, the group said: "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.
|Whelan on FA investigation in Mackay|
|"We have spoken to the FA. There is nothing in the pipeline. I don't think there is anything really to investigate."|
"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 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."
Jason Roberts, a former Wigan player and now an anti-racism campaigner, wrote on Twitter he was "disappointed" with the appointment and expressed hope that the FA would enforce a "zero tolerance policy towards any form of discrimination".
In response, FA managing director Adrian Bevington said: "Football has the platform to lead. Thinking discriminatory is as bad as making discriminating comments."
Whelan said he thought the FA investigation would come to nothing.
"We have spoken to the FA," he said. "There is nothing in the pipeline. I don't think there is anything really to investigate."
He added: "I did ask Malky questions about the problems he has had.
"He was up front. He told me the absolute truth. I totally and utterly believed what he said.
"We have all done things wrong. We are not all saints.
"He has earned the right to another chance to do what he does best, managing a football club."
On the prospect of being charged by the FA, Mackay said he would deal with any punishment that came his way.
|Recent Wigan managers|
|Uwe Rosler||December 2013 - November 2014|
|Owen Coyle||June 2013 - December 2013|
|Roberto Martinez||June 2009 - June 2013|
|Steve Bruce||November 2007 - June 2009|
|Chris Hutchings||May 2007 - November 2007|
|Paul Jewell||June 2001 - May 2007|
"I'm a big man," said the former Scotland international, who arrives with Wigan struggling near the foot of the Championship.
He added: "I would ask people to judge me as they see me.
"I made mistakes but I'm absolutely not racist. I hope going forward the people of Wigan see me as I am."
Mackay was sacked by Cardiff in December 2013 but was linked with a return to management with Crystal Palace following the departure of Tony Pulis at the start of this season.
However, Palace abandoned plans to appoint the 42-year-old when details emerged that the former Watford boss had sent text messages that he later admitted were "disrespectful of other cultures".
No timescale has been placed on the FA investigation.