Most places it's always been the case, that sales tax always applies. Some like NM have exemptions for not ready to eat food items, but the garage sale is supposed to pay tax.
The funny thing is, there is no real way to pay it in NM unless you get a state buisness licence. The intent is to get those who have a buisness in their home, to get a buisness licence and pay the tax. Tax may not apply to mail order, but that loophole is being closed in more places. I think the city ordinance is 4 garage sales a year max, to discourage under the table second hand stores popping up in R1 neighborhoods.
The idea behind any crackdown, is to go after folks who run a flea market or out of the garage buisness off the radar.
When I was making a whopping 3 thou a year as a furniture and pottery artist, I had to have a buisness licence and pay tax. Part of the process was proving that my buisness activity wasn't going to make life hell for my residential neighbors.
I thought it was kind of funny, that it didn't matter how bad I was starving, I still had to collect and pay sales tax. A lot of my fellow craft market vendors really resented this tax, and I never could get it through thier heads that the customer paid it, not them. But after collecting the tax for three months, there were sure times I had a hard time coughing it back up to make the payment, on a 3 thou a year income. The day I had to send that check, it sure hurt a few times.
Regarding the Louisiana law, I smell a crackdown on the gun show with that one.