The vaccine does not have negative efficacy against Omicron. We don't have very solid data here because Omicron is so new, but one recent paper indicates that in a household setting a booster prevents around 50% of Omicron cases. That's not as good as with Delta, but it's not nothing and it's certainly not negative.
> The negative estimates in the final period arguably suggest different behaviour and/or exposure patterns in the vaccinated and unvaccinated cohorts causing underestimation of the VE. This was likely the result of Omicron spreading rapidly initially through single (super-spreading) events causing many infections among young, vaccinated individuals.
That's from the linked paper. The authors don't claim at all that the vaccine has negative efficacy, and the study is simply not set up to measure that anyway. You cannot draw this conclusion from the data in this paper.
Assuming that Denmark vaccinated oldest/most vulnerable first, this could be a confounded estimate (because age both means you got the vaccine first, and that your immune system will be less effective against Covid).
Personally, I think it's a statistical fluke, and was going to argue that it must be due to a smaller sample size until I saw the width of the confidence intervals (CI's get narrower as observations increase).
Very odd, and I'll be surprised if that makes it through peer review intact.
It stands to reason that the unvaccinated at this point are in large parts hermits who are "protected" by their lifestyle. However, it's also plausible that the non-neutralizing antibodies from the vaccine induce a suboptimal immune response with Omikron.