How did Sai Baba's life and practices make it impossible to categorize him as strictly Hindu or Muslim?

Chapter 7 of the Shri Sai Satcharitra explains this paradox in detail. While Sai Baba resided in a mosque, a typically Muslim practice, he maintained a sacred fire (Dhuni), allowed the ringing of bells and blowing of conches, and had a Tulsi Vrindavan, all of which are Hindu traditions. He was described as looking like a Yavana (Muslim) if called a Hindu, yet bearing the noble marks of a Hindu if called a Yavana. The text notes that while his ears were pierced in the Hindu fashion, evidence of circumcision was also apparent. Ultimately, the chapter concludes that not an atom's worth of trace could be found to definitively place him in either group, as his incarnation was holy and beyond both.