Is there any source in encouraging a man who identifies as Jewish but isn't so Halachically, to marry a Jewish woman and raise a Jewish family?
For instance, a patrilineal Jew although he isn't Jewish, if he is a cultural Jew and wishes to continue his Jewish family's legacy should he still be disuaded from marrying a non-religious Jewish woman? Is there a religious duty or source to have Jewish children?
Note: I ask because I am aware that a convert who is patrilineally Jewish has a slightly different status to a regular convert as he has the status of 'זרע ישראל' and is considered “מקרב אחיך" according the Aruch haShulchan in Choshen Mishpat 7:1.