Is there a way to do a DNA test anonymously?

My first thought is that your DNA (encoded in a high resolution) is itself a unique identifier attached only to you. You expose yourself to being found by blood relatives however distant, as well as swept into criminal investigations that involve blood relatives (however distant).

It seems totally reasonable to be wary - it's a comparatively new field that generates data that can be held indefinitely and re-analysed later as additional techniques are developed, potentially without consent. The privacy laws around it are new and relatively untested, there are few to no discrimination protections yet, and it increases your chances of crossing paths with law enforcement regardless of any wrongdoing on your part.

I'm not going to judge people who still choose to go ahead, that's very much a personal choice based on how much those factors concern you, but making an educated call on what you're comfortable with seems the absolute opposite of overreacting!

I did a bit of looking around the same question myself a while back. My bar for judging a company that's actually serious about privacy would be a similar attitude to Proton or Mullvad: "we can't disclose what we don't know, so we encrypt everything we can in a way that even we can't access, and would actively prefer it if you don't tell us who you are". I did find one company that claims this is "coming soon", but the site raises several red flags for me. In an ideal world the only point of trust required would be an audit ensuring that the sequencing machine itself immediately encrypts the output with your public key and does not store or expose the raw data anywhere, and that the sample is then immediately destroyed.

Depending on your personal risk tolerance, there's nothing (other than presumably the site T&Cs, depending on how much you care about that) to stop you from buying a mainstream test with cash or a prepaid card and submitting it under a pseudonym. The question then becomes how worried are you about the data being linked back to you anyway by correlating it with relatives' data and/or other factors?

One big problem is that DNA, by its very nature, is uniquely identifiable information. By definition it can't be anonymous.

Even if you found the DNA testing version of a no logs VPN and paid via cash, you're still trusting that they are telling the truth.

Any testing you get done based on promises of anonymization now will likely be held in perpetuity. So in 5 or 10 years, if the company that did the test gets bought or changes their mind and adds your results to a database, you're out of luck.

(Re-reading this comment it comes off as a bit tinfoil hat, but that's kind of what OP is asking for. I think DNA tests are great and the fact that so many decades old cold cases have been solved via genetic databases is fantastic. But people should definitely know what they are signing up for when they get a DNA test done.)