No state allows sibling marriage.
I guess you were trying to take a dig at The Boot, but to seriously answer your question, sibling marriage was banned there from its first laws, those being codified in 1808, four years prior to its admittance as a state in 1812. I had to check the correct date to use there, but it appears that its admission as a state had no bearing on the laws it had already adopted and codified. I thought maybe everything sort of "reset" if you become a state and you have to institute a new round of laws, but apparently not. That makes more sense why we've got so much Napoleonic Code left over.
And if we're talking about the land itself, and not the "state" as such, both French and Spanish civil law governed the area before it was purchased as a territory, and both already prohibited sibling marriage. So the real answer is.....I'm not sure....further back than I know how to quickly find. Prior to 1803 when it was acquired from France. But since we can say that the laws were technically redone when Louisiana adopted the Digest of Civil Laws in 1808 and that is the basis from which all state law originates today, I'll say 1808.