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The 31-year-old Stoke City winger shared on Instagram Stories a screenshot of one user sending him DMs calling him a "stupid ginger" and making reference to the IRA.
"Don't make me set your house on fire and burn everyone inside it," reads another message.
In response to the abuse, McClean took to his Instagram page on Friday to release a lengthy statement.
The Republic of Ireland international said: "Banging my head against a brick wall here but look I have been doing that anyways for a long time so one more won't make a difference.
"So much coverage this past couple weeks about discrimination and the condemnation of it across media outlets, players, ex-players etc which is great to see because it's wrong and idiots should be held responsible for their actions and words as nobody should be subjected to that.
"Make no mistake about it or to take anything away from that but just to pose the question really, racism, gender, ethnic... the list of discrimination that goes on is unacceptable right, my question is here... does being abused for being Irish and anti-Irish abuse acceptable? Is it not popular enough to be seen to be knowledged [sic] or spoke out about too?
"I have highlighted the abuse publicly on social media recently and the silence from everyone is deafening!
"If you are offended by me saying that, then maybe that tells you something, 'We are not criminals, we are Irishmen! This the crime we stand accused...'"
Instagram last week announced plans to hit accounts with strict penalties should they send out vile abuse to other users.
The social media platform, owned by Facebook, has confirmed that accounts could be removed from Instagram as a measure to help deter footballers from receiving abuse.
Arsenal hero Ian Wright also admitted his disappointment in the fight against racism earlier this month after an Irish teenager who racially abused him avoided a criminal conviction.
Featured Image Credit: PA/Instagram
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