We are not at Gattaca levels of DNA predictions, not merely because of lack of tech development, but because the DNA doesn't actually tell us that. Given the weak clues that DNA actually gives about the individual, Gattaca is a cautionary tale about what happens when people believe too much in bad predictions, and enshrine bad models as a metric of social worth. Any society could fall prey to this, but today it seems more likely the bad models will be based on predictive modellijg from monitoring social media than from DNA.
Federal research programs also bit too hard on the promises as well, and invested heavily in genome-wide-association-studies (GWAS) to very little effect. I chose my HN username as these were getting deployed, much out of frustration with that direction of research. The clues, even early on into a massive spend, we're that GWAS wouldn't be terribly productive.
I think the biggest risk of being oversold right now are the "polygenic risk scores" being used for various quantitative traits, which fail to generalize very well. As more advanced machine learning techniques are used, we are likely to get even worse models. The curse of dimensionality makes the problem much more difficult than with traditional machine learning fields. Each case with a single label has millions of features, but we only get a very small number of cases relative to the number of features. And we are unlikely to be able to transform our feature space in ways that have worked well for, say, images by using spatial data. My personal hypothesis, by no means unique to me, is that we need to use the network of gene interactions as the feature transformation, but we don't yet have that network explored fully.