The Republic of Ireland international has refused to wear the poppy around Remembrance Day since 2012, a decision which has resulted in a decade of widespread abuse.
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McClean was booed by Swansea fans during the 2-2 draw with Wigan on Saturday and, last month, the 33-year-old shared clips of anti-Irish chants at Sunderland.
Speaking in October, he wrote on Instagram: "For my son, who is seven years old and watches every Wigan game… to be asking his mother, 'why are they booing and singing that song at Daddy?' And to have to tip toe around answering him is something which should not be happening.
"This post is not one for sympathy [trust me, it is not wanted] but one of anger. Considering every single year we have an FA representative come into each club to discuss the same old crap they spew to us about discrimination. Every single year, I challenge them on the abuse. Every single year, they do nothing.
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"This clip is one [from] yesterday, which can be heard clearly of one particular chant, as well as other chants of 'f*** the pope and IRA', being sung by the majority of the 30k crowd, as well as numerous individual chants of 'fenian b******, fenian c***', 'you dirty Irish c***'.
"[This was] while displaying a tribute before game honouring Niall Quinn, who is also the same nationality as myself. Couldn't make the stupidity up.
"Now, everyone who attended the game would have heard this loud and clear including the referee, match officials and other officials! I should not have to report every single incident when clearly they can all hear what I hear, and they should be doing their job by taking action!
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"I would be lying if I was to say I expect anything to be done about this by the FA and EFL [history shows this] but here is another chance sure. And I certainly don't expect any action to be taken by Sunderland themselves, given they did nothing when I was their player."
McClean has previously explained he would wear the poppy if it only remembered WWI and WWII victims - but as it is a universal symbol for the defence of freedom, his stance is a result of the British Army's actions in his native Derry in 1972, when 26 unnarmed civilians were killed on 'Bloody Sunday'.
When asked about the abuse suffered by McClean, Rangers and Scotland legend Souness told talkSPORT: "We live in a democracy. If he's beeing booed at a football game, or things are being sung about him, that's not nice.
"It's not nice for his wife or his kid, it is totally wrong that him and his family are being threatened.
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"That's abhorent. But it will just be keyboard warriors and village idiots.
"But you also have to understand that 10,000 Irish soldiers lost their lives in the Second World War - and I think it's right we remember them.
"You know what side of the fence I'm on. I managed a Protestant institution in Glasgow Rangers and we were royalists.
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"Going back a month, there was a small element at several football grounds up and down the country that rejoiced in the death of our Queen. That's unacceptable.
"There is nothing the FA can do about that, but that happened. So James has to get on with it.
"It is very much his right to choose to go down that road, but I'm afraid this will not go away for him.
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"It will be an annual thing he has to take on the chin because he has chosen to go down that road."
McClean was listening and sent a message to Souness via talkSPORT host White.
The Irishman said: "Jim, can you tell Mr Souness with regards to his 'get on with it' advice - I got on with it for a very long time until it became not just me but my family.
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"It is one thing taking abuse, but when your family gets involved, it means a totally different thing.
"I would suggest if he's not in a position to talk about it as I am, then he doesn't appreciate the level of abuse I have to endure."
However, Souness doubled-down and insisted McClean must face the repurcussions of his choice.
"I accept that," Souness responded. "Once it impacts on your family, it must be very difficult. But this is something he has to deal with.
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"This was his choice. Maybe he should go back to when he first made this stance, maybe someone said, 'This will not just be about you going forward'. And that is the case."