"Kennedy, commonly known by his initials RFK Jr, has a history of spreading health information that scientists say is false."

https://www.bbc.com/news/articles/crlne0n191wo

It contains a link leading to another (older) BBC article titled:

"RFK Jr: How anti-vaccine misinformation has shaped his 'truth-teller' candidacy".

https://www.bbc.com/news/world-68447223

In it, you can read an anecdote about a mercury-based preservative, used in some vaccines, called "Thimerosal", as related by vaccine researcher Paul Offit:

"Prof Offit confesses he was excited to be able to talk a Kennedy through the studies, which showed children exposed to Thimerosal (not found in most US vaccines anyway since 2001) were no worse off than those who hadn't had exposure. But a year or so later, Mr Kennedy wrote an article published in Rolling Stone magazine which repeated baseless claims that Thimerosal was causing health problems."

A NEJM study does conclude that no harm comes from exposure to Thimerosal (and that ingesting mercury may even be ... beneficial)?

"Results: Among the 42 neuropsychological outcomes, we detected only a few significant associations with exposure to mercury from thimerosal. The detected associations were small and almost equally divided between positive and negative effects. Higher prenatal mercury exposure was associated with better performance on one measure of language and poorer performance on one measure of attention and executive functioning. Increasing levels of mercury exposure from birth to 7 months were associated with better performance on one measure of fine motor coordination and on one measure of attention and executive functioning. Increasing mercury exposure from birth to 28 days was associated with poorer performance on one measure of speech articulation and better performance on one measure of fine motor coordination. Conclusions: Our study does not support a causal association between early exposure to mercury from thimerosal-containing vaccines and immune globulins and deficits in neuropsychological functioning at the age of 7 to 10 years."

https://www.nejm.org/doi/full/10.1056/NEJMoa071434

On this kind of basis, concerns over Thimerosal became a baseless conspiracy theory, industry got Nennedy's RS article retracted, and the BBC can portray Kennedy as a loon.

Is he, though?

This is the Merck Safety Data Sheet on Thimerosal:

"Very toxic by inhalation, in contact with skin and if swallowed. Danger of cumulative effects. Very toxic to aquatic organisms, may cause long-term adverse effects in the aquatic environment.

(https://web.archive.org/http://www.merck-chemicals.com/documents/sds/emd/int/en/8170/817043.pdf)