The problem with a Hainan independent republic if the Red China exists in this ATL is that probably it would be easily conquered, in OTL Hainan the last stronghold of Kuomintang in China (apart of Taiwan) was easily conquered in a brief campaign that lasted only a pair of weeks in 1950, at the difference of Taiwan, the island of Hainan is too much near of the chinese continental coast to avoid an amphibious operation from Red China (while that Taiwan need a truly serious amphibious effort because the distance that separates the island from continental China, Hainan was occupied by a massive although improvised fleet of all kind of ships that transported the People´s army to Hainan).
In my personal opinion, I think that a different warlords period in 1920´s with some warlord making of Hainan his feud and making a serie of reforms (even some kind of alliance with french authorities in Indochina) that mades of Hainan some kind of stable warlord state could work better, in OTL Kuomintang although made a serious effort to unify all China, also in some cases prefered to pact with some warlords in exchange of his help against communists, with the focus of KMT in his North Expedition, the KMT could decide made a treaty with the Hainan warlord, we could develop some kind of ATL where from this POD: a different warlords chinese period of 1920´s the final outcome would be an independent republic of Hainan.