The info below is my understanding of the situation in Louisiana, though I would not pretend to be an expert on Louisiana state law.
First, there is no law in Louisiana that specifically allows homebrewing, nor one that specifically bans homebrewing. Homebrewers are not considered producers, and therefore don't fall under the jurisdiction of the Louisiana ATC. Since there is no state law specifically addressing homebrewing, the state defers to federal law on homebrewing (note: this is not generally true for other states).
Businesses with licenses to sell alcoholic beverages due fall under the jurisdiction of the ATC. There is a law on the books that states that businesses licensed to sell alcohol for on premises consumption (such as restaurants and pubs) may not serve unlicensed alcohol. The ATC interprets this to mean that licensed establishments cannot allow homebrew to be served on their premises.
HB1484, if passed, would create an exception to this through a special permit that will allow licensed businesses to host homebrew club meetings, competitions, etc. The permit is free, and must be granted by the ATC to any licensed business that applies for it. Each permit lasts for three days, but the bill does not establish a limit on the number of permits a business may apply for. It does mean that the business would have to apply for a separate permit for every individual club meeting, competition, etc.