hamlet's development spirtually/ philosophically

Our protagonist, Hamlet begins as a firm protestant. we infer this because his mother begs him "to go not to Wittenburg" (act1 scene 2) - a key place in the protestant reformation. He regards his soul as "a thing immortal" (act 1 scene 4).
However, his confidence in this worldview deflates after he sees the ghost of his father coming from purgatory, a concept only held by Catholics. When he first sees his father's ghost he believes it is either an angel or a demon bringing "airs from heaven or blasts from hell" (Act1 scene 4) but does not seem to believe he is a ghost. After the ghost assures him that he is his "father's spirit" (act 1 scene 5) and tells him of his uncle's wicked actions, Hamlet disregards his previous denial in ghost existence and goes forth to fufill his task of vengence.
This initiates his play-long struggle to find what to believe comes after death. Previously he lamented over society's point of view believing that he could not end his life for that would land him in hell. He wished that "the Everlasting had not fix'd his canon 'gainst self-slaughter!" (act1 scene 2). Seeing and hearing his father's ghost on top of all his other trouble brings him to question whether living is really worthwhile debating over it better "to be or not to be" (act 3 scene 1). In this debate we sense his new uncertainty when he states, "for in that sleep of death what dreams may come when we have shuffled off this mortal coil must give us pause" (act 3 scene1). However it is evident that as he goes deeper into his plot for vengence he has taken on a Catholic worldview because he chooses to not kill the king while his is praying out of fear that he would then then "send [his uncle] to heaven" (act 3 scene 3).
After killing Polonius Hamlet goes through a period of naturalistic thought seeing death simply as a return to the dirt where everyone comes from. While in the graveyard he describes how to "trace the noble dust of Alexander, till he find it stopping a bung-hole" (act 5 scene 1).
Towards the end, however, after the death of his beloved Ophelia who commits suicide, he shifts back to Protestantism disregarding omens and believing once again in Divine Providence. Before dueling Laertes Hamlet senses trouble but resigns to God's will and acknowledges "a special providence in the fall of a sparrow" (act 5 scene 2). This is the solution of his worldview struggle as Horatio, also a protestant, suggests that he is sung to heaven by "flights of angels" (act 5 scene 2).