Most claims of 'the other side' is lying are themselves lies. It's mostly people just spinning things to suit their own personal biases (without necessarily even realizing that's what they're doing). For instance the vaccine topic is one I did a deep dive on not too long ago when deciding which vaccines to approve for my children. This [1] is essentially the bible of vaccines - it's a massive study across a large sampling of evidence for all major vaccines, carried out by the National Academies of Science. I'll quote them:
----
The vast majority of causality conclusions in the report are that the evidence was inadequate to accept or reject a causal relationship. Some might interpret that to mean either of the following statements:
- Because the committee did not find convincing evidence that the vaccine does cause the adverse event, the vaccine is safe.
- Because the committee did not find convincing evidence that the vaccine does not cause the adverse event, the vaccine is unsafe.
Neither of these interpretations is correct. “Inadequate to accept or reject” means just that—inadequate. If there is evidence in either direction that is suggestive but not sufficiently strong about the causal relationship, it will be reflected in the weight-of-evidence assessments of the epidemiologic or the mechanistic data. However suggestive those assessments might be, in the end the committee concluded that the evidence was inadequate to accept or reject a causal association.
----
The overwhelming majority of the rhetoric around vaccines, including from governmental figures, is doing exactly what they warn against. There's simply a lot of nuance on most of every issue worth discussing, that people often don't want to acknowledge.
[1] - https://www.nationalacademies.org/projects/PHPH-H-08-17-A/pu...