When a layperson hears this, they'll think that there's a small but possible chance that vaccines do cause autism; when what the scientist means to say is that "it's highly unlikely that vaccines cause autism."
What's more important IMHO, is raising the general understanding of how this science works and not falling into the trap of feeling like we have to debate this buffoonery on the same level. We're so worried about being called "elites" or whatever that we fight on their terms instead of just straight up calling it out as stupid and manipulative and giving it no more time than that.
;-)
I got sent some looping tik tok anti vax thing with a pretty woman saying sincerely vax bad, with no sources and links. The people influenced by that are not going to look up the papers in Nature.
The real issue isn't scientific caution. It's that the misinformation campaigns exploit any uncertainty, no matter how small. The solution isn't dumbing down science communication, but being clear about what the evidence actually shows.