If I take a DNA test, can it incriminate a relative I've never met?
Yes. This is one of the genuinely unsettling implications of consumer genetic testing, and it has become a real-world thing.
The most famous case is the Golden State Killer, identified in 2018 after decades on the run. Investigators uploaded crime-scene DNA to GEDmatch (a public ancestry database) and identified distant relatives of the killer. From those distant relatives, traditional genealogy work narrowed the search until the killer himself was identified, arrested, and convicted.
The implication: you don't have to take a DNA test for your DNA to be in a searchable database. If a third cousin you have never met takes a test and uploads to a public database, your own DNA is partially identifiable through them.
There are now studies estimating that for most Americans of European descent, enough of their distant relatives have already tested that they could be identified through familial search even if they personally never took a test.
How seriously you should take this depends on what you mean by "incriminate." If you are a person of interest in a serious crime where DNA evidence exists, yes, familial DNA search is a real and growing investigative tool. If you are an ordinary person with no criminal exposure, the practical risk is minimal - but the privacy implications are still worth thinking about.
Different ancestry companies have different policies about cooperation with law enforcement. Some require warrants. Some have open databases. Read the terms before you upload.