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Short answer
This is a blatant lie.
Not only are DNA tests legal in Israel, but one of the biggest companies in this field was also founded in Israel. Its name is MyHeritgae.
This is quite an idiotic lie conceived by pro-Palestinians to somehow claim that Jews do not allow DNA tests in order to hide that they either do not belong to the Jewish ethnicity (Ashkenazi or Sephardi) or that their origin is from Europe or elsewhere.
While it is true in many cases that Jewish ancestry can be traced back to various regions, this is irrelevant to Jewish ethnicity and, therefore, to their ability to immigrate to Israel.
