Content Warning: We're talking about issues involving race, colonialism, cultural appropriation, and history of people who weren't writing their own history at the time all this happened. I'm also not a full-on historian, just a tikiphile who's also interested in keeping my fandom of the genre respectful, so consider this amateur work. I'm 100% hopeful someone with better context can fill in the gaps and/or correct me here.
Background:
The American "Tiki" scene (I'm going to use Polynesian Pop Culture or PPC from here on out) got started before WW2 with some themed restaurants that became wildly successful on the west coast. The earliest on record is Don the Beachcomber's, a restaurant started by the son of a prohibition-era rum bootlegger named Ray Gantt who eventually changed his legal name to Donn Beach. His restaurant was decorated with "beachcomber" style artifacts (nautical, tropical, vaguely referencing prior ideas like Robinson Crusoe, etc) and featured a menu of mostly Cantonese cuisine with made up names (Crab Rangoon anyone? Rangoon - now Yangon - is a Tibetan city, far from the ocean with help from /u/sukritact adding context, Yangon is coastal, but the dish is absolutely not traditional or from the city, and cream cheese was never a traditional Asian ingredient) and riffs of traditional Caribbean rum-based drinks with likewise fantastical marketing names.
The other major known influence was the restaurant and resulting chain named Trader Vic's, created by Vic Bergeron in Oakland, California. The restaurant was originally known as "Hinky Dink's" in 1934 and featured an Alaskan adventure theme, but quickly converted to a nautical theme as Vic discovered Don the Beachcomber and loved the gimmick.
Check this link out for more info on how this all went down, and pay particular attention to the second photo, which is ca. late 1930s Don the Beachcomber's Hollywood restaurant. Note the lack of Polynesian-influenced imagery - it's just bamboo, plants, and Japanese fishing floats. No tapa cloth patterns, no "tikis," nothing like that.
https://www.foodrepublic.com/2016/10/24/inside-don-the-beachcomber-the-original-tiki-bar/
The PPC influence came later, with the rise of post-war interest in the South Pacific. Some early broad cultural references were the Rogers & Hammerstein film "South Pacific," a musical reinterpretation on the James Michener novel "Tales of the South Pacific," a huge hit both in literary and musical form, as well as Thor Heyerdahl's 1947 Kon-Tiki expedition and subsequent 1950 documentary film and book.
That, combined with stories from American GIs returning from the Pacific theater seemed to create a gestalt imagining of a tropical paradise.
I'm not sure exactly when the PPC imagery got blended in, but it was definitely some time in the early 1940s - Trader Vic's famous drink the Mai Tai was created in 1944, and the same phrase was used to name a separate drink in Donn Beach's notebook possibly as early as 1933. "Mai Tai" as a phrase is definitely of Polynesian origin, regardless of the origin story of the drink, with Vic's story claiming the name came from a Tahitian friend who was an early taste tester of the concoction - so by 1944 there was already some Polynesian influence at least in the naming of food and drinks.
https://beachbumberry.com/recipe-mai-tai.html (Jeff Berry is the historian of tiki drink recipes, and is pretty much the authority on historicity of when these things happened. Read his notes here on the origins of the Mai Tai drink.)
Getting to the timing of when Polynesian imagery started being imported into the emerging American "tropical bar" trent, the most interesting to me is the "Goof," the mascot of a bar called Christian's Hut on Shelter Island in San Diego, which got started during the filming of "Mutiny on the Bounty" in 1935. I don't know when the "Goof" mascot got started, but by all reports it's earlier than the "tiki" imagery that resulted when Christian's Hut was rebuilt in the late 1950s as Bali Hai in the same location. This link has a photo of the Goof on the back of a panel van in 1953:
https://classicsandiego.com/restaurants/christians-hut-san-diego/
The final thing to mention here is that in 1959, Hawaii was brought officially into the United States as the 50th state (along with Alaska). US interests, along with the rise of air travel opened up tourism to Hawaii in a way that had never happened before. American interest in the South Pacific was never higher, and tourists were bringing home Hawaiian carvings of pre-Christian gods as souvenirs (many, probably most, of which weren't artifacts, but were carvings made by native Hawaiians for the tourist trade.)
PPC and its implications:
Now we're late 1940s moving into the 1950s and for whatever reason, Polynesian cultural imagery is now incorporated into the American tropical bar trope. The bars got bigger and more elaborate - the biggest of which boasted floor shows with native Islander entertainers performing traditional dances and staging full floor shows with hula, fire dancing, drumming, and other cultural performances from Polynesian cultures all across the Pacific. There is one remaining giant palace from those days, currently closed due to rain damage over the last year, but with all intentions of re-starting service once some investment can be found if anyone wants to travel and see what things were like then - it's in Fort Lauderdale, Florida:
Bartenders, likewise, were in large part from the Pacific, but many were of Filipino, not Polynesian, heritage. Mario Licudine of the Mai Kai, became famous after serving as staff bartender at Don the Beachcomber's for over a decade. A lot of the other bar staff were also Filipino.
https://www.maikaihistory.com/2017/07/27/mariano-licudine-the-houdini-of-the-liquids/
Some more history for context:
The idols, ancestor images, and god carvings were almost entirely cultural, not spiritual art by the time of the American PPC explosion. European colonialism and the spread of Christianity had for the most part wiped out a lot of the spiritual traditions of Polynesian cultures. There were (and are) some holdouts - in particular (from my experience - I don't have a lot of scholarly reference here - people who have more please add in!) New Zealand Maori culture managed to hang on to a lot of its oral history. There's a huge difference in visiting Hawaii versus New Zealand in how Polynesian imagery is handled - In Hawaii, there's a lot of tourist and pop culture imagery (less now than there were in the 50s) compared to New Zealand where there's more of a living tradition. Hawaii does have some cultural continuation, but the plantation and exploitation was more complete in the Hawaiian islands from what I've been able to put together.
Responses I've seen:
I've been to several "Tiki" scene history discussions, particularly focusing on the Mai Kai and its family business history - at this point, the family who runs the Mai Kai is pretty much of Islander descent - a lot of care was taken by the founders to represent its heritage and staff well, to the point that the founders married Islander people and their descendants are operating the place now. The interviews and comments were all positive - promoting Pacific cultures, outreach, etc.
Personal comment: from a family business whose prosperity is based on the business, this is understandable. But I'm a white dude who is only relaying what I've heard - I am not in any position to pass a value judgement.
I haven't seen any direct commentary particularly of mid-century contemporary responses from Islanders.
There's some scholarly study that I'm aware of, but I have not had the opportunity to read much of it. Some older, some very modern. A lot of the earlier study was focused on the impact of tourism in general to Polynesian identity. I've not seen a lot specifically referencing American tropical bars and their use of PPC. Here's some links I've had bookmarked for a while - I can't get past the paywalls and/or they're books I have yet to read:
https://www.jstor.org/stable/25169171
https://www.atiner.gr/journals/tourism/2014-1-2-1-Caneen.pdf
https://www.academia.edu/30777117/The_Cultures_of_Tiki
The next-to-last is available behind an odd login wall, but has an excellent reading list and is well cited.
There's TONS of modern commentary, from apologists within the tiki community as well as criticism from both within and without. That's pretty easily available from a Google search. I'd love to see contemporary comments if anyone has them - American culture in the mid-20th century was definitely not recording much sentiment from Islanders, although looking at the Hawaiian tourism angle might be a good route to dig up adjacent opinions.
Edits over time to fix typos, links, etc. I also removed a "this isn't a super comprehensive" disclaimer 'cause I wound up going way more in depth than I thought I would.