While I'm not very familiar with thimerasol, some reading tells me that it's only used in certain influenza vaccines.

https://www.cdc.gov/vaccinesafety/concerns/thimerosal/index.html

https://dph.illinois.gov/topics-services/prevention-wellness/immunization/thimerosal-vaccines-q-a

mRNA vaccines are new technology, so the Covid-19 mRNA vaccines are actually the first approved mRNA vaccine technology. So, mRNA vaccines were not used in the past. Thus, I don't think anyone has ever done the comparison of post-vaccine autoimmunity between mRNA and other vaccine types.