The Northern Ireland Equality Commission (N.I.E.C) took the bakery to court on behalf of Mr. Gareth Lee, who is a volunteer activist for the QueerSpace organisation. The N.I.E.C is part of the Department for Culture, Media and Sport, an arm of the UK government.
This judgment is in effect, saying that the bakers are not allowed to act according to their beliefs. It is saying that there is an official set of government sanctioned beliefs held by some and then there are other, so called "backward" ones held for example, by Ashers Bakery. It is those "backward" beliefs that the state will prosecute you for holding.
There’s a word for that kind of society: Totalitarian.