What does the NEC say about antioxidant compound on aluminum conductors?
The NEC has no section that says apply antioxidant to aluminum conductors. What it has is Section 110.3(B), which requires listed or labeled equipment to be installed and used in accordance with any instructions included in the listing or labeling. If the lug, connector, or splice device you are using has instructions that say to apply a listed joint compound, then applying it is mandatory and skipping it is a 110.3(B) violation. If the connector is listed for use without compound, and many modern ones are, then you are not required to add it.
Read the connector instructions, not the internet
Compression connectors from the major manufacturers are frequently supplied prefilled with an inhibitor sealed under a cap or a tape. Those need nothing added. Many mechanical set screw lugs are listed for aluminum without compound, and their instruction sheets say so explicitly. A handful of older mechanical connectors and most field-applied compression sleeves for direct burial still call for it. There is no universal answer, which is exactly why 110.3(B) points you at the paperwork in the box.
When compound is called for, use a product listed for the purpose. The instruction sheet will typically name a compound or reference a listing category. A random tube of dielectric grease from the parts store is not an equivalent. Some antioxidant compounds are conductive and carry zinc or other particles intended to abrade the oxide film during tightening. Getting that on the insulation or into a device is messy but harmless. Getting a non-listed grease into a connection can be worse than nothing.
The rule that actually matters more: AA-8000
Section 310.3(B) requires solid aluminum conductors 8, 10, and 12 AWG, and stranded aluminum conductors 8 AWG through 1000 kcmil, marked as AA-8000 series electrical grade aluminum alloy conductor material as specified in the standards. The old AA-1350 series that gave aluminum branch circuit wiring its bad reputation in the 1960s and 1970s is no longer permitted for these applications. AA-8000 alloy has creep and thermal expansion characteristics much closer to copper, which is why properly torqued modern aluminum feeders perform well.
Torque is the other half of the job
Section 110.14(D) requires terminations to be tightened to the manufacturer specified torque value using a calibrated torque tool where a torque value is provided. This is not optional and it applies to copper and aluminum alike. A loose aluminum lug will fail no matter how much compound you applied. Wire brush the conductor if the connector instructions call for it, apply the specified compound if required, land the conductor, and torque it to the marked value.
Field takeaway
No blanket NEC requirement for antioxidant. Follow 110.3(B) and the connector instructions. Use AA-8000 series aluminum building wire per 310.3(B). Torque every termination to the marked value with a calibrated tool per 110.14(D).