First of all, some of those are no longer used in vaccines (or in all vaccines). Second of all, trace amounts of some of those things, or compounds in which those things are bonded, are not harmful to humans. I mean, chlorine is poisonous to humans, but it's a major component of table salt. As far as mercury, it's actually ethylmercury – a less toxic compound found in trace amounts in vaccine preservative thimerosal – that was used (as opposed to the toxic methylmercury). But it's been removed from everything but certain flu vaccines since 1999 (and you can still ask for a thimerosal-free flu shot for no extra cost). A person is infinitely more likely to get unsafe amounts of mercury from eating seafood than from a vaccine.

And for the record, the other "core issue" is the unfounded belief that vaccines cause autism (which is not supported by any science, but the autism-scare anti-vaxxers also believe all scientists are part of a conspiracy, so…)

Tell me someone explained to this person that vaccines just prepare your immune system for the disease.