Mr White said that one officer claimed that under the Prevention of Terrorism Act he was within in his rights to confiscate the mobile phone on which the photos were taken.
He said the police officers took his details and he was eventually allowed to leave.
By Monday morning, more than 4,000 people had "liked" the campaign page, external which had been set up on Facebook.
Supt George Nedley, of Renfrewshire and Inverclyde division, said: "I can confirm we have received a complaint regarding this incident and one of my senior officers has spoken to Mr White regarding this.
"As a result a full review of the circumstances surrounding the incident and the allegations made is under way."
A spokesman for Braehead said: "Staff at an ice cream stall in Braehead became suspicious after they saw a male shopper taking photographs at their counter.
"The staff thought the man had also been taking photographs of them and they alerted one of the centre's security staff."
He added: "The member of security staff approached the man and politely asked if he had been taking photographs. Because of the nature of the incident, police became involved and also spoke to the man.
"Our priority is always to maintain a safe and enjoyable environment for all of our shoppers and retailers. The member of our security staff acted in good faith.
"We have a 'no photography' policy in the centre to protect the privacy of staff and shoppers and to have a legitimate opportunity to challenge suspicious behaviour if required.
"However, it is not our intention to - and we do not - stop innocent family members taking pictures."