IgG4 is the class of immunoglobulin responsible for shifting immune response upon encountering some antigen from attack to tolerance, which is good for false positive pathogens like flower pollen that cause seasonal allergies. But that's of course not the type of response one would want from their immune system when encountering SARS-COV-2, since if the viral particles are being tolerated as opposed to being cleared by one's immune system, it leaves the viruses uninhibited to multiply and continuously damage your body.
IgG4 response is how your body would typically treat things like allergens that are basically harmless and don't need a full immune response. Covid needs a full immune response, and an IgG4 response suppresses that. You don't want your body to treat a virus the same way it treats pollen.
The others did a good job of the technical details. The higher level implication is that taking too many of the shots will appear to make you feel better in the short term but create long term internal damage, as the immune system won't fight the virus as effectively/at all and instead will let it get on with replicating.
So it seems the shots convert short term but temporary unpleasantness into long term serious problems - at which point, of course, they will be classed as not vaccine related because they didn't happen immediately.
As such the social implications of this discovery are more of the same. The population will continue to be split into camps that think all vaccines are perfect and reject any link with bad outcomes as not proven, denied by public health so it must be false. Public health bodies will continue refusing to break down incidence data by vaccine status, or will do so in fudged ways by redefining what "vaccinated" means. Other people will observe long term disparate outcomes between people who had lots of shots and others who had none, but if they try to speak about what they see they'll be shut down, told it's just anecdotes and not data and maybe fired. Polarization will continue to spiral.
Overall: this finding is bad, and the long term implications are bad.