I forgot to mention genetic confounders from this paper, which inflate the shared environment influences relative to heritability.

Firstly, assortative mating results in both parents carrying traits that correlate with tattooing, which shrinks the differences between identical and non-identical twins, meaning genetic effects are "masked" and attributed to shared environmental effects. This mechanism is mentioned briefly in the paper.

Secondly, homophily (or assortative friendship): People choose friends who are more genetically similar to themselves than random members of their ethnic group. Typically the relationship is genetically equivalent to third cousins. This means that the shared cultural environmental effect on tattooing is also genetically influenced.

Homophily wasn't accounted for in the twin study and I have no idea how one would even begin to calculate the effects of this. The paper included neither multivariate genetic analyses nor polygenic scores, so direct genetic correlations and indirect genetic effects could not be quantified.

Anyway, the rapid rise of tattoos could be due to the fact that significant proportions of the population are "genetically primed" to embrace this social contagion. These members of the population cluster together, become influential on social media or in other entertainment, and then negatively influence otherwise normal members of the population. Edit: leftism spreads the same way.