If someone has verifiably non-observant or non-Jewish ancestry(their mother and her mother etc for several generations were practicing Christians) but a DNA test shows matrilineal jewish DNA, are they halachically Jewish?
The question was modified after I first answered to add the case of verified nonJewish ancestry. Given that, the duplicate question applies. If there is no nonJewish ancestry, then the answer below applies.
DNA testing is not treated as aidus for a particular matter. However, the problem with nonobservant ancestry might be if a male within the line married a nonJewish woman (who did not convert halachically) or a woman in the line was divorced and remarried (without a valid get) in which case all the descendants would be mamzerim. Even if one nonJewish woman was in the line, the DNA test would probably not detect that. Similarly in the case of an invalid divorce, the DNA test would definitely not detect that. I did know of someone who had a question as to his ancestry so he was megayer misafek, because the question was far enough back that it could not be proven absolutely. In any case, if there were no divorces (which does not affect the halachic Jewish status) or intermarriages, the person would be halachically Jewish and not a mamzer.