The two-sentence complaint, released to Family First under the Official Information Act, said the group was "a religious based pressure group" with the sole purpose of preventing human rights for non-heterosexual people.
Mr McCoskrie said the board's decision was an abuse of power which showed government groups were being used to enforce an ideology.
He said the board had investigated only one charity which opposed Family First's views, and that group was still registered.
"The Charities Registration Board should be consistent - but it's quite evident that it's not, and is using isolated complaints by disgruntled people to muzzle groups who challenge the prevailing politically correct view."
Under the Charities Act, registered charities can undertake political activities, such as supporting or opposing legislation in its area of activity, but not as its main purpose.
The former Charities Commission - now the Charities Services arm of Internal Affairs - has investigated Family First's charitable status twice, in 2008 and 2010, and concluded it fitted the criteria.
But the Charities Registration Board this month found the group's main purpose was to promote particular points of view about family life.
An Internal Affairs' spokeswoman said Charity Services had been in communication with Family First since 2008 regarding advocacy and activities that may not have been consistent with the Charities Act.
"In 2012, it came to Charities Services' attention that some of these activities were happening again. This prompted another review of Family First's activities and purposes.
"Reviews of this nature are instigated when activities come directly to the attention of Charities Services, or in some cases a member or members of the public alert Charities Services."
A number of high-profile groups which publicly advocate on policy have charitable status, including the Child Poverty Action Group and Amnesty International.
But other groups have been deemed too political for charitable status, including the Sensible Sentencing Trust and the Council for Civil Liberties.