There is no aluminum in baking soda. The misunderstanding that there may be was begun by an advertising approach of Bob's Red Mill Aluminium-Free Baking Soda. As a consequence of announcing on the label that it was aluminum-free it led many to conclude that other brands contained aluminium. This was, however, untrue. Bob's Red Mill directly extracts the sodium bicarbonate from the ground whereas other manufacturers of baking soda use chemical reactions between soda ash and carbon dioxide to produce the baking soda.
Aluminium is not produced or in any way a part of this process. However, baking soda produced by the Solvay method results in pollutants that are problematic and may conceivably leave residue in the baking soda as it is limited in percentage of purity and produced in varying grades for multiple uses. In contrast, the alternative natural deposit trona process is at least 99 percent pure.
Baking powder on the other hand can contain aluminium because of differences in the manufacturing process between baking soda and baking powder.
"The Solvay method ... of producing baking soda ash is widely used, it is also problematic because the chemicals used in the process are pollutants and cause disposal problems. An alternative is to refine soda ash from trona ore, a natural deposit." (MadeHow.com)