The greatest problem creating lack of trust is inability to have open scientific debate about the issues. Too many dr's have been silenced if they have differing opinions. Couple that with lack of information provided to get informed consent are just a couple of the issues causing hesitancy for many.
A lot of information coming out has been twisted if it doesn't support the approved narrative. This leads to a breading ground of conspiracy ideas as people try to figure out why these things are happening.
It doesn't help when you see inconsistency such as Walmart being allowed to stay open while the local hardware store had to shut down.
Most, if not all large corporations were considered essential, while smaller local owned had to shut down during lockdowns with many ultimately being forced to close permanently. This made many wonder about government institutions making decisions for us.
Pfizer should have simply released all data for the public instead of being forced to by the courts. That's yet another thing to cause hesitancy.
Health care should be a decision between dr and patient, especially with something experimental.
Regarding dna changes... I've seen it argued both ways. But, anything credible gets deleted very quickly and has to be posted on some off the wall sites. That's why we need open and free debate to regain public trust in our institutions.