A video has emerged that shows a Free Presbyterian minister criticising the DUP for selecting Alison Bennington to stand in the council elections.
In a sermon last month, Rev John Greer of the Free Presbyterian Church in Ballymena, referred to the party's decision to choose her.
In response, the DUP said its position remained "unchanged".
"We support the current definition of marriage," a party spokesperson said.
Speaking after her election last week, the DUP's Belfast East MP Gavin Robinson, said it was a "good news story", despite DUP assembly member Jim Wells claiming members were "shocked by the decision" to let her run.
In Rev Greer's sermon from 21 April, prior to the local government elections, he said that Christians were "being conditioned into thinking that things that were once reprobated are now acceptable... such as sodomy."
He described that as an "agenda".
"Now we have the DUP putting up their candidate, who is an out-and-out lesbian, that's what I mean," he said.
"My friend that's what Paul (the Christian apostle) is talking about here, that's the kind of thing that's going on in our own little land, and there we have before our very eyes, what God has to say about the danger of an ungodly world - a corrupt world influencing even the thinking of people who should know better - and have them accept what God abhors."
When asked for comment, Rev Greer told BBC News NI that the remark was part of a wider sermon, and that the message he was preaching was "not specifically crafted to deal with that issue", but rather, commentary on how Christians should be living.
He said it was not his place to dictate to the DUP about their choice of politicians.
"If a party which once took a decision begins to move away from it, it's my duty as a Christian minister to highlight that," he said.
Rev Greer said the Bible was his "final authority" and said the Free Presbyterian Church had issued a statement ahead of the council elections criticising all political parties that attempted to "normalise and promote marital and sexual relationships that are in contravention of the clear teaching of scripture".
Although the DUP and the Free Presbyterian Church were never formally linked, the Church was set up by the former DUP leader Ian Paisley and provided many of the party's first candidates.
Under Ian Paisley, the party opposed same-sex marriage - a position it insists it continues to hold, despite the selection of Ms Bennington as one of its candidates.
Many DUP members also remain members of the Free Presbyterian Church.
It has also been reported that DUP councillor John Finlay wrote to party officers to say that Mr Paisley, "must be turning in his grave" about the DUP's selection of an openly gay politician.
The letter, obtained by a number of media outlets, said the DUP's choice of Alison Bennington to stand for election in Glengormley had been "foolish" and sent "confusing signals to our support base which has consistently welcomed our strong stand on LGBT issues".
Mr Finlay told BBC News NI that he would not be making further comment.