"It is attempting to imply that the Catholic Church and The Vatican condone same sex marriage despite no formal communication of said claim.''
Other complaints to the authority mirrored that view and said the advertisement mocked the Catholic religion.
The authority's chairman Jenny Robson said the advertisement was referring to the issue of the same-sex marriage bill that was before Parliament and was legislation the Catholic Church opposed.
The electricity company used irony and humour, in keeping with Powershop's same power, different attitude campaign, she said.
Ms Robson said she acknowledged the offence caused to the complainants, but the billboard did not reach the threshold to be said to cause widespread offence in light of prevailing community standards.
"Neither did it breach the due sense of responsibility to consumers and society.''
Powershop chief executive Ari Sargent welcomed today's decision.
"It kind of reflects the feedback that we've got from the general public - yes, there was some vocal opposition but, by in large, people saw it for what it was and didn't find it particularly offensive.''
The company wanted to "stimulate debate'' about the issue, Mr Sargent said.
"Obviously it's not our intent to offend people.''
Labour MP Louisa Wall's Private Member's Marriage [Amendment] Bill has passed its first reading and submissions are being heard by a select committee.
Powershop has courted controversy with other billboards, such one as depicting former Iraq president Saddam Hussein collecting charity and former North Korea dictator Kim Jong-il selling hotdogs for charity.
