Ashers Baking Company tried to overturn a previous court ruling that they acted unlawfully when they refused to decorate a cake with a pro-gay marriage slogan.
The Evangelical Alliance surveyed evangelical Christians and in September 2016 respondents were asked whether: "A business should have the right to refuse to print, publish (or write in icing on a cake) a message with which it does not agree."
89 per cent of evangelical respondents agreed, and 56 per cent agreeing strongly.
Six per cent opted for neither agree nor disagree and five per cent disagreed.
The company in Belfast was told to pay £500 in May after it refused to bake the cake for a customer on the basis it went against its Christian beliefs.
Gareth Lee was told a cake decorated with the slogan Support Gay Marriage alongside the Sesame Street characters Bert and Ernie could not be processed at their bakery.
The judge found that Ashers had acted unlawfully and directly discriminated against Mr Lee on grounds of his sexual orientation and political beliefs.
Daniel and Amy McArther, the owners, then appealed the verdict against the Equality Commission for Northern Ireland.
Their appeal failed.
Simon Calvert from the Christian Institute, supporting the McArthurs, told Premier they thought their case is strong.
He said: "We're confident that the case that has been put forward on behalf of the McCarthur family... is a good case.
"Most people whether they agree with the McArthur's Christian faith or not, most people don't think equality law should be used in this way, to try and force people to try promote causes that they disagree with."
He went on: "It's simply to do whether you should be forced to promote someone else's message - and I think that most people think you shouldn't have to do that."
Speaking outside court before the verdict Daniel McArthur said: "Over two years have passed since our family business said it was not able to help campaigners who want to change the law on marriage in Northern Ireland.
"We have always said, and say again today, that whilst we are unwilling to endorse a view that goes against our conscience, we will continue to happily serve anyone who comes through our doors – whatever their background, lifestyle, or beliefs.
"This has never been about the customer. It has always been about a message promoting a cause that contradicts the clear teaching of the Bible on marriage. A message promoting a cause with which I and my family fundamentally disagree.
"We hope and pray that today, this Court will send a different sort of message – one which protects the freedom of people like us and of businesses like ours to remain faithful to their conscience.
"It won't be much longer now until we all know its judgment, and after that we may be in a position to make some further comment."
Listen to Premier's Hannah Tooley speak to Simon Calvert here:
