Officers have received pictures of people dressed in offensive costumes at Airdrie District Orange Hall and Social Club.
The images, which were posted on Facebook but have since been removed, including a man dressed as Hitler giving a Nazi salute posing with children wearing a yellow star, which Jewish people were forced to wear in Nazi Germany.
Another image showed a man dressed as the Pope with a noose around his neck while a further picture showed two men holding a toy wearing a Celtic strip between them at crotch level.
The photographs were published on the Whinhall True Blues Flute Band Facebook page and reportedly date from 2010 and 2013.
A Police Scotland spokeswoman said: ‘’The information has been passed to relevant officers to establish the facts and identify any criminality.
“Police Scotland takes all reports of hate incidents seriously and will investigate such reports appropriately and proportionately.”
The images were passed on to police by The Sunday Herald.
Robert McLean, executive officer at The Grand Orange Lodge of Scotland, told the newspaper he had “no comment to make” on the images.
The Grand Orange Lodge of Scotland later posted a comment on social media criticising the media coverage but failing to address the images shown.