Sports fans were told to remove the button badges at the gates by security guards because "they represent a protest".
Some people at the Green are believed to have been told they could wear the badges if they were kept out of view.
Glasgow 2014 Venue Regulation 6.18 states that no flags are allowed to enter a venue - or the vicinity of any Games venue - if they are normally associated with causes, affiliations or organisations.
Neill Patton, from Glasgow, said: "My Yes badge is not offensive, it is not a protest - it simply represents my personal view."
A spokesman for Yes Scotland said: "Organisers of the Commonwealth Games quite rightly want to keep politics out of the Games."