It "forced" her only in the sense that she believes, quite bizarrely, that providing flowers for a civil wedding ceremony makes her complicit in "sin". If one thinks homosexuality is a sin, then by all means, don't practice it. But if you say you provide flowers for weddings, buck up and do what you say you'll do.
Implicit in the Christian consideration that marriage is between one man and one woman, one might well find a homosexual civil union is not a marriage. Therefore, the performance of a ceremony invoking that civil union is not a 'wedding' as defined within the belief system. If you look at:
Leviticus 18:22 - Thou shalt not lie with mankind, as with womankind: it [is] abomination.
or
Leviticus 20:13 - If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood [shall be] upon them.
those are pretty clear Old Testament references to the unsuitability of such civil unions within the Christian belief system--not simply forbidden, but an abomination.
Now, in deference to modern times, no one is casting stones--at least Christians aren't, in Islam punishments get more creative when the act is prosecuted.
Would the court have been equally hasty to fine Muslim florists?