They didn't sue her...at first. Their story reached the ears of WA's AG Bob Ferguson (D) who sued Barronelle under the WA Consumer Protection Act which forbids discrimination due to being a homo among other things. The two homos involved then joined the suit either out of ideological conviction or a desire to get some money out of the situation.
Not that it matters much but Barronnelle's shop is in Benton County, WA, which turned down a recent referendum approving same sex marriage by about a 2-1 margin (it passed statewide).
It appears Ferguson is out to crush Stutzman as an example to others that they will not oppose the homosexual juggernaut and its Democrat enablers. Consider this: the WA State Constitution stipulates (Art I, section 14): Absolute freedom of conscience in all matters of religious sentiment, belief and worship, shall be guaranteed to every individual, and no one shall be molested or disturbed in person or property on account of religion; but the liberty of conscience hereby secured shall not be so construed as to excuse acts of licentiousness or justify practices inconsistent with the peace and safety of the state; but neither that provision, nor the 1st Amendment of the US Constitution has made a smidgen of difference in this case.
Liberal Fascism at its finest.
Well if they had any decency they could have told the AG they did not want to join the suit and would testify in her defence.