One can be secular and still be a lapsed Jew. One cannot hold another religious faith such as Chrstianity, Islam, Buddhism, or atheism and still be a Jew. That person is an apostate.
But they would remain ethnically Jewish whether they followed the Torah or not. The State of Israel recognises Jews for their ethnicity as well as their religious activities. Just because someone is not an orthodox religous Jew does not make less entitled to refer to themselves as "Jewish" or get automatic citizenship of the Israeli state as a Jewish person.