People from the Republic of China (i.e., Taiwan) with English language proficiency don't refer to themselves as 'island China' or 'the real China' (barring fringe elements), but may call themselves (ethnically) Chinese. Generally though, they call their country Taiwan and themselves Taiwanese in English.

Besides, if ambiguity is the concern for people from the PRC, the phrase "I am from the People's Republic of China" lacks any political subtext.

Expecting mainland Chinese to use the formal name of the PRC to self-identify is needlessly clunky and formal.

The reason why many Chinese, regardless of nationality, use the phrase “mainland Chinese” or “mainland China” in English is because it’s the direct translation of 中国大陆, the phrase used to identify the mainland. It doesn’t indicate political affiliation in any way.