..has no aluminum, last time I checked. Other brands of baking powder did contain it.
Baking soda would not contain aluminum except by contamination.
Just as Morton Salt contained no aluminum, last time I checked, but other brands of table salt do.. IIRC it was "aluminum silicate" added for free-flowing in several brands of salt other than Morton. Water softener salts I have no idea what they might use, but if I were using a water softener, I'd be finding out and acting accordingly. I don't know about road-salting salts, but that's another thing to consider environmentally.
I use Celtic Salt sole whenever I use salt for eating or body care, so it really doesn't affect me.
All in all, I have observed that the longtime traditional brands are less likely to be contaminated than newcomer brands, for instance, 20 mule team borax, arm & hammer, Morton Salt. It's more likely to be the more recent, off-brands that have wierd stuff in them. JM $.02 .
I have studied Hulda Clark 's excellent work for many years now and have read every word she has ever published.
I think I recall seeing that note about baking soda too, in one of her books years ago and, knowing already the differences between bleached, unbleached, self-rising and non-self-rising flours and baking ingredients and baking soda-&-salt instead of baking powder, etc., I recall laughing to myself and marking it as a typo, saying to myself "Hm, somebody doesn't know how to cook, that's why nobody caught this :)".
Don't worry about your Arm & Hammer. It's good stuff. IMO its benefits far outweigh the small possibility of this concern.
For instance, getting rid of cancer. Read of the great work of Dr. Tullio Simoncini in Rome, Italy, using baking soda to heal cancer here: