By "China," I am referring to the Mainland, Hong Kong, Macau and Taiwan collectively, without regard to geopolitics. Is there a word that refers to this entire region that would not offend any Mainlanders, Taiwanese or citizens of the Special Administrative Units?
maybe "大中華區". most multinational corporations used this term to describe the regions you mentioned.
such usage is correct, in context of nowadays, or recent decades. historically, taiwan was integrated into the chinese empire after ~1683. before that time, formosa was colonised by the dutch, spanish.
last, and most importantly is: how do you define "chinese speakers".
there're many ethnicities in "greater china" can speak chinese, they've their own cultures, languages and ideas of state / nation. so, "politically neutral" is, imo, unattainable.
it's better to seek a term that's vague, fuzzy enough; that no-one want to waste time and effort to argue its precise definition.
I agree that "大中華區" is quite common for this issue. There are other expressions such as 兩岸三地(中、台、港) or 兩岸四地(中、台、港、澳)
"大中華區" is a bit vague to me, because it might include Chinese speakers in Singapore and Malaysia. The concept of this word varies from organization to organization.
Maybe the question is: Why do you want to describe Mainland China, Hong Kong, Macau and Taiwan collectively? What's the topic? For instance, if you want to compare Chinese-speaking music or films in this region, you can use"華語圈"(Chinese-speaking area) it's very common to say 華語流行音樂 or 華語電影.