I think that the Chamorros of the Marianas would provide a good template to follow. Based on that, the Hawaiians would be forced to follow Catholicism; New Laws or not, religious fanatics like the Spaniards would not allow paganism to be openly practiced, and OTL the kapu system could not survive the disruption of contact anyway. However, a lot of their traditional religion would survive as informal "superstitions", with religious practices folded into veneration of the saints or traditional medicine. A native Hawaiian identity and culture will survive to the modern day, but it will be very Catholic and possibly less united than OTL, as an early conquista will butterfly the Kingdom of Hawaii period and perhaps lead to a stronger cultural attachments to pre-kingdom era political organizations (i.e. "I'm a Waimean" and "I'm a Molokaian" instead of "I'm Hawaiian").
The Spanish themselves are not going to heavily exploit Hawaii initially; in the Pacific, the trade with China was their one goal almost to the point of myopia. Oahu will be established as a resupply station for the galleons, and the other inhabited islands will probably receive one catholic mission and one corresponding fort to defend the mission, and not much else. I thought about the Spanish using it as a naval base to launch punitive raids into Asia, but the Philippines are a lot closer and better suited for that purpose so I guess that it's a silly thought.
The makeup of the islands going into the modern times depends entirely on if the Spanish eventually do decide to bring Hawaii into the plantation economy. If so, the islands could end up as OTL with a minority Hawaiian population and majority of people descended from Philippino immigrants brought in willingly or not to work the sugarcane fields. If the islands are not turned into giant plantations, the human population is majority Hawaiian and the infrastructure still geared mostly to feeding people locally, with a lot of small terrace farms, fishponds instead of artificial sand beaches, etc.