The family of William Kenneth Wilson, who died in 2012, wanted it on his headstone at St Oswald's in Dean to mark the 40 years he had devoted to Freemasonry.
However after taking their case to the chancellor of the diocese, it was decided it would be "detrimental" and "inappropriate" to allow it.
Speaking on Premier's News Hour, the Archdeacon of West Cumberland Ven Richard Pratt defended the decision.
He said: "There's a suspicion that freemasonry substitutes something else for God the Holy Trinity.
"They have other names for it - 'the great architect', 'Jahbulon'.
"It's seen as a mixing up of different religion and it's seen as Gnostic and there are levels of knowledge and you move through the ranks - the more you know the higher rank you have. Christianity has been opposed to that since Gnosticism was first around.
"Christianity is something that's open - everyone can read the Bible, everyone can attend Church...there aren't ways of ascending towards God by gaining knowledge - the only way we can access God is through Jesus himself."
There are an estimated six million Freemasons worldwide.
Most church groups have spoken out against the group however there are several church leaders, including bishops, who have become members of the group.
Listen to Premier's Marcus Jones speak to Ven Richard Pratt here: