David Quinn is a founder of the Iona Institute, a newspaper columnist and a regular media commentator.
During the marriage equality referendum campaign, David said that
Should the referendum pass, a same-sex couple could demand a right to marry in a church ... In Denmark, we have already seen that the Lutheran Church, a State Church admittedly, has been forced to conduct same-sex weddings.
At the time, lawyers pointed out that there was no basis to imagine that the then-proposed referendum, now passed, could be used to force Catholic or other churches to conduct weddings outside their own internal rules, just as they have not been forced to marry divorced people since the 1995 divorce referendum, and no attempt has been made to do so.
The Lutheran Church in Denmark is an established government-run church; its governing body is the Danish parliament, and the Minister for Ecclesiastical Affairs (currently Mette Bock, a member of the Liberal Alliance party) is an MP and member of the Danish cabinet. An established church is a branch of the government. The word 'forced' means that one entity had its behaviour unwillingly constrained by another, but here there is only one entity.
Some clergy of the Danish church had been conducting informal same-sex weddings since the 1970s. Same-sex marriage was approved in Denmark in 2012, and as an arm of the state the Church in Denmark began to carry out such services on a legal, formal basis at that time.
David is correct that the Christian Institute, a campaign group which concentrates on opposing LGBT rights, is registered in the UK as a company, although this appears to be against company registration rules.