I highly doubt that it's possible to publish such data anonymously. There are less than ten billion people, about 33 bits are enough to identify everyone individually. If you publish a couple dozen genetic markers you almost certainly have very few people who share the same pattern.
Fascinating, thanks for a great link. Could publishing health research data in the opposite direction help?
Today we hand medical researchers large databases pre-filled with the data they seek.
As we move into a world of increasingly ubiquitous biometric monitoring, asymptotically trending towards real-time, could the data gathering be flipped around instead? Individuals become the only ones who own their detailed DNA profile (the profile with billions of base pairs stored), held on either a personal device with suitable encrypted backups (ideal) or held on their behalf by a trusted service (encrypted with a key only the individual holds). Researchers send out requests for specific data ("weekly blood pressure of males between 20-60, with these genetic markers, starting now/5-years-ago"). Individuals either manually approve matching requests or set up approval "subscriptions"/rules. Requests matched with data sources get anonymized data of course.
Researchers not only can get data this way, they get a continuous, crowd-sourced data feed. Longitudinal studies might get easier to set up through this kind of channel. There isn't a way to ID someone by their feed and the researchers' requested, limited matching genetic markers alone, unless an attacker systematically breaks into multiple research databases, and starts building a Palantir-like correlation amongst all the hacked databases; that dramatically raises the detection risk to the attacker. Another attack is an overly-broad set of genetic markers in a single request, and those requests can be auto-denied before even getting into the brokering system. Short-term, we can prohibit the collection of any part of the 13-base-pair CODIS markers, though long-term we have to assume that CODIS or its future successors will eventually expand to a larger set of markers (and in the far, far future, possibly the entire sequenced genome).
See http://33bits.org/2009/12/02/the-entropy-of-a-dna-profile/