Actually Thimerosal was used as a preservative for MMR vaccines - though not in the vaccine itself. Now the mercury compound it contained gets excreted with no impact on the body, but there was mercury in a sense. Though you are correct about conflating the various risks.
Removing thimerosal makes vaccines harder to store, and so increases their costs, but who cares, right?
It is still in some flu vaccines (not ones for kids) so perhaps we have a time travel memory also, in that getting a flu vaccine at 30 causes autism at 4.
I’ve seen stupider contentions.
I posted the classic picture of the Hindenburg exploding, and noted that they hydrogen that caused this disaster is in water, and so we had best do something about this dangerous situation RIGHT AWAY!!
That’s reasonably close to the mercury situation.
The CDC cite says it was never used as a preservative for MMR https://www.cdc.gov/vaccinesafety/concerns/thimerosal/index.html - but I’m open to the idea that I’m misunderstanding something.
And here we have the bottom line.
You are open to the possibility. Most of us here are open to it too. The problem folks are not. Either they’re actively selling something to the rubes with no care for the facts, or they’re motivated by ego or psychosis rather than intellectually honest curiosity.
Returning to the OP’s dilemma, better scientific explanations will not reach people who are more interested in defending their righteousness than they are in learning something. The fix for people like that is to prevent them from breeding and / or to train their kids correctly in schools so they don’t have ego (or psychosis) as their primary personality trait.
Good luck with that little project. 
My impression is that a lot of the sellers, along with the rubes, have absolutely no concept that many careful published studies showing, for instance, that there is no link between vaccines and autism count for more than knowing someone who claims this. The sellers are as dumb as the rubes - they are motivated by having something to sell.
As for preservative - I consulted my local expert, but I suppose it is possible that there were no preservatives. She spent a lot more time researching this stuff than I did. Or I could have misunderstood. (We’re both sick and not hearing well.)
The idiots are now worrying about strands of dna in the vaccines, or impurities, or any trace “contamination.” I bet they don’t realize how much rat feces are in their organic food.