Taiwan Society
Although there are many people who are either centrist or unconcerned, Taiwanese society is very polarized by allegiance between followers of the two major political blocs colloquially known as the "Pan-Blue Coalition" and "Pan-Green Coalition." Pan-blue supporters are more likely to favor the idea of (re)unification or keeping the status quo with China, while pan-green supporters are more likely to support the creation of a formally independent Republic of Taiwan, among other differences, to simplify a highly complex situation.
Despite certain correlations, it is extremely dangerous to infer anything about a person's political beliefs from what you believe to be their background. Since the word "mainland China" is frequently used to exclude Hong Kong and Macau as well, it is less likely to offend anyone than calling the PRC "China" alone.
Most Taiwanese will react negatively if the Republic of China is referred to as "Taiwan Province" in its entirety. In some professional settings, the term "Greater China" is acceptable. However, keep in mind that there are so many nuances and complications involved that you have already entered a minefield if you are discussing these topics. But regardless of one's political views, calling the island Taiwan is acceptable because that is what locals call it. Titles like "Republic of China" are exclusively used in formal contexts.
