The Creggan born Republic of Ireland player does not wear a poppy on his shirt for games scheduled around Remembrance Day.
The 30-year-old has refused endless abuse for not wearing the poppy over Bloody Sunday in 1972 when British soldiers shot dead 14 unarmed civilian protesters.
Barnsley were charged by the Football Association on 3 January for alleged sectarian chanting against McClean.
“James McClean was once again subjected to disgraceful anti-Irish and sectarian abuse this weekend,” said Kick It Out after the weekend’s goalless draw.
“We have informed the FA so they can investigate but we reiterate – the abuse he continues to receives is absolutely unacceptable and shames our game.
“Greater action must be taken by the authorities to safeguard his and his family’s wellbeing, because the current situation cannot continue.”
Championship side Stoke last week released a statement of support for McClean, who joined the club in July 2018.
The Professional Footballers’ Association (PFA) also issued a statement at the start of January.
It has responded to the latest incident by stating: “There is no justification for this or any other type of abuse and the PFA stands fully beside every player who faces discrimination.”
Stoke City boss Michael O’Neill also condemned the abuse hurled at James at the recent Barnsley fixture in the Championship.