No. Tirthankaras are not required to be born in a Jain family. Most Tirthankaras are said to have been born in royal or noble lineages, especially the Ikshvāku dynasty (kingly houses), but not exclusively within a Jain family. In fact, two Tirthankaras are described as belonging to different lineages (Harivamsha/Yadu lineage) in some traditions.

• The common Jain view: many Tirthankaras come from Ikṣvākuvaṁśa (the Ikshvāku dynasty), not from a Jain lineage per se. This is true for the majority of Tirthankaras across Digambara and Śvetāmbar traditions. ( jainknowledge.com)
• Exceptions noted by some sources: Munisuvrata and Neminath are sometimes associated with different lineages (Harivamśa/Yadu) in certain accounts. This distinction appears in some traditions and texts. ( jainknowledge.com)

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