The detailed chemistry of anaerobic adhesives can be quite complex and subtle. The adhesives are mixtures of acrylic monomers which polymerise easily by free-radical mechanisms. The free radicals are generated by decomposition of an organic peroxide. However, if there is oxygen around it reacts with the radicals and stops the polymerisation from happening. That’s why the adhesives are stored in polythene containers which allow oxygen to permeate.
The other important factor is that metals like iron and copper are very efficient catalysts for decomposition of peroxides to make free radicals, so that if the liquid adhesive is trapped between two surfaces containing iron or copper then radicals are produced rapidly, oxygen is used up through reaction with those radicals and can’t be replaced, and fast polymerisation (adhesive curing) takes place. Aluminium does not catalyse peroxide decomposition, so if the surfaces are aluminium then removal of oxygen still allows polymerisation to take place but the absence of catalysis means it’s a lot slower. The aluminium oxide is a bit of a red herring – even soluble aluminium compounds are not catalytic.
In reality it’s a bit more complicated because the requirements for long-term storage and efficient curing are challenging and need all sorts of additives to get the required control, but those are the basic principles.