On Saturday someone ripped a cross from the billboard outside St Matthew in the City.
The church's latest billboard depicts a "gay-dar" showing a spectrum from gay to straight. The cross acted as a gauge.
The church is known for stirring debate and hopes the sign will highlight discrimination in the Anglican Church against members of the gay and lesbian community.
A caption at the bottom of the billboard states: "As used by the Anglican Church to assess potential priests."
New Zealand Anglican bishops refuse to consider any candidate for ordination who is gay or lesbian and in a committed relationship.
St Matthew's is running an online petition asking the Anglican Church to stop this practice.
Church vicar Glynn Cardy said there was no way of telling if the missing gauge was an act of vandalism or the actions of a drunk who thought it was a fun thing to do.
He said the billboard has generated several phone calls and emails - both positive and negative.
The negative "tend to be quoting pieces of scripture of the dictionary" while the positive were "thank you" and "well done".
Cardy said he'd also heard from a scientist who said the billboard highlighted discrimination on the basis of genetics.
"I thought that was a very interesting take."
Bishop Philip Richardson of Taranaki said until the Anglican Church can agree whether homosexuality is a consequence of "wilful human sinfulness" or an "expression of God-given diversity", sexual orientation would continue to be a deciding factor in determining potential priests.
But Priest Associate of St Matthew's the Reverend Clay Nelson says he is amazed that with all the information and science available in this modern age that the church can still argue sexual orientation is a matter of wilfulness.