Taiwan kept much of the traditional Chinese values and culture, as well as kept parts of the Japanese culture after WWII. The Japanese culture was from 1895 - 1945, and Chiang Kai-Shek ensured that the traditional Chinese culture was kept after 1945.

The Cultural Revolution destroyed much of the traditional Chinese values in mainland China, so CKS ensuring the Chinese culture living on in Taiwan was a positive.

Starting in the 90s when the emergency measures were lifted (Taiwan was under a de facto martial law from 1949 to 1989), the Western influence (maybe cabal influence) eroded the traditional values. Since the 2000s, homosexual stuff was promoted, and traditional family values were subtly attacked.

Taiwan's politics is complicated. The left leaning DPP in power is actually the one defending Taiwanese sovereignty, while the right leaning KMT wants unification with CCP China.

There is actually no right solution for the Taiwanese issue. And Taiwan was actually purposely left in a sovereignty limbo by the major powers after WWII. The San Francisco treaty in 1952 only stated that Japan renounced the sovereignty rights to Taiwan, but did not specify who has the rightful claims to Taiwan (ROC vs PRC vs USA). The US actually had planned to annex Taiwan as one of its protectorate after WWII, but General MacArthur was busy setting up democracy in Japan that he didn't have time to look after that, and then the Korean war happened. The ROC and its remaining military being in Taiwan since 1949 was seen as an acceptable solution by the US as a way to setup a first line of defense against Communist China.