The Catholic Church is not at all some sort of ideally liberal institution, and while she is 'liberal' in a somewhat-Classically Liberal sense, it is not because she thinks that such is the nature of man. There is no absolute, non-culturally- and non-socially- relative line which we can draw between “public acts” which fall under the jurisdiction of the community and might get punished by the state and “private acts” which any decent right-thinking person keeps his nose out of just so long as the shades are drawn.
The liberal principle of Catholic social teaching starts by asserting that error and evil have no rights, absolutely speaking. The sword of the state is there to punish wickedness in general – potentially any wickedness – for wickedness in general affects us all, but that there is some evil the correction of which would cause more harm than good. This was the Church Fathers’ reason for continuing to allow slavery, even though almost none of them thought it was a good thing in itself. To abolish slavery would at that time have brought down the entire economy and cast thousands upon thousands of former slaves loose in the society without adequate social, political, and familial ties that would allow them to live decent lives. (This was also the reason why SS Thomas and Augustine argued against outlawing prostitution: another evil we’ve been able to get rid of -ish.)
But of course the Church has never considered slavery a positive good, just a necessary and tolerable evil, so when the moment arrived that the economy of the world no longer relied upon it, she cheered on those who worked to abolish it. And we today consider it a good thing that slavery is outlawed and no longer part of our society and economy.
So the judgment of which evils we tolerate and which evils we do not is relative to the amount of harm we would cause in a particular society by attempting to stamp it out in that society. Our judgment of the nature of a particular evil is not relative, but our judgment of the tolerability of that evil quite definitely is.
So to be frank, given the right sort of society and the right situation, we should probably vote to outlaw fornication, whether between man and woman, man and man, woman and woman, or what-have-you, and punish it by some power of the state. But it’s pretty clear that we don’t live in that society, nor anything like, so people knockin’ da boots in the wrong bed don’t really have to worry about Christians trying to enforce that bit of the moral law.
But let’s stop pretending that the Catholic Church has ever said that the state has “no business” telling people what to do about particular things. She has said quite the opposite, over and over again.