In the United States the sales tax regulations are done by the state (though some sates do allow cities or counties to piggy back on those taxes).
Regarding online sales, a vendor like Amazon maybe required to collect and forward to the state sales tax depending on:
- does the state tax online sales.
- does the state only require sales tax if the vendor has a presence or Nexus in the state.
As of now New Mexico uses the Nexus test, and Amazon doesn't have one in the state. So they don't collect sales tax.
If you go to a brick and mortar store in New Mexico they will collect sales tax, unless the item falls into a category that is tax free.
There have been calls for the US congress to pass a law to make online sales not depend on the determination of having a Nexus.