I agree aluminum & mercury are neurotoxins.

My understanding is that adjuvants are needed to produce an "immune" (allergic) response from an inert "pathogen".

I admit I haven't researched the topic of adjuvants extensively, but it makes sense to me that a truly inert bit of organic matter probably would not produce an immune reaction.

The distinction to the claim you made is that I am skeptical that modern vaccines can have any immune effect without these adjuvants (even if manufacturers were willing to spend more producing each dose). Moreover, we should consider whether the immune effect is net beneficial even if it can be induced.