Nigel Williams from Southampton said he would be prepared to do work for Joanne Lockwood, but refused to do work for her business, SEE Change Happen.
According to the business's website, it specialises on "equality, diversity and inclusion advice and services to organisations and business" with its primary focus is on LGBT+ support.
The Christian Institute, which is supporting Williams, said he and Joanne Lockwood met for the first time at a weekly business event on 5th September, in which Williams spoke to attendees about his Christian faith.
The charity said the two met for the second time at the same business event on 26th September and later that day, Williams received an email from Lockwood enquiring about a possible order for a "business venture promoting a particular model of diversity".
Williams declined her request via email because he did not want to promote a cause which he believes may marginalise Christians.
A spokesman for the Christian Institute said: "For years we've warned of growing hostility towards people with mainstream Christian views. The terms 'equality', 'diversity' and 'tolerance' have been twisted out of all recognition in an attempt to marginalise, shame and punish Christian people.
"Nigel Williams made it crystal clear that he would be prepared to do work for Jo Lockwood. Indeed, his email said: 'I am very happy to print for you'. However, he was not prepared to do work for a business that actively promoted a cause which might impact negatively on those with a Christian faith' ".
According to The Times, Lockwood has been living as a trans woman since January and was "gobsmacked" at his reply.
She told the paper: "I was not expecting a lecture. I disbelieved this could happen in 2017. I have been distraught and cried and my wife consoled me."
In a statement to Premier, Lockwood said: "In all of this I only want to promote diversity and acceptance for all individuals, and the right for us all to live our lives fairly and without rights or opportunities being denied. This has been the focus of my new business and my personal life since transitioning earlier this year.
Lockwood said he wasn't looking for a fight, but was upset when she was "met with silence, followed by personal upsetting attacks from others in the business community" after requesting for the business cards to be made.
She continued: "I fully respect everyone's right to their own faith, beliefs and to enjoy religious freedom. I would never want to compel anyone to do work which ran contrary to their own beliefs.
"...I will unflinchingly stand up for all trans people in a world which still has a long way to go in its treatment of minorities."
The Christian Institute has called this situation "chilling" and "unnecessary".
The charity pointed out that the dispute is similar to that of Christian-owned Ashers Baking Co., which went to court after declining to decorate a cake with a pro same-sex marriage campaign slogan.
Aidan O'Neill, leading barrister for the case, said such disputes open "the floodgates" for more, citing a Christian baker refusing to take an order to make a cake celebrating Satanism, and a printing company run by Roman Catholics declining an order to produce adverts calling for abortion on demand to be legalised.
He said: "It is a fundamental tenet of free speech and freedom of belief that people should not be forced to help promote causes flatly contrary to their own deeply-held views."