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In what way could they possibly affect dental health?
They might perhaps, just, conceivably decrease resistance to periodontal disease but that would take decades to show up (since it's a very slow disease process) and would be likely to be so subtle as to be almost un-provable.
There have been some anecdotal reports of tooth sensitivity post COVID vaccines, but I could not find any hard and fast evidence in the literature. The VAERS (vaccine adverse reaction system) does mention that some people in the trials had tooth pain, but of course we can't say that's because of the vaccine.