As Srivaishnavas must not worship other demi-gods, why do we worship Hanuman? Is he a Prapanna or Bhakti yogi or a Mumukshu?

Hanuman is not a demi-god; he is called Siriya Tiruvadi. As he is always with Rama, Sita, and Lakshmana, while we worship them, we must worship Hanuman as well. Hanuman as one who lives long (Chiranjeevi), even now resides at mount Gandhamadana.