Checking from names who answered this question I think I should answer it b/c I am Mainland Chinese. I am from a province that speaks the same dialect as Taiwanese and I can easily tell from their accents whether they are Taiwanese or mainland Chinese.
From my experience I feel Taiwanese is much more sensitive than Mainland Chinese. They don't like it when you say "Taiwan, China" (as if you say "Taiwan, part of China" and emphasize the latter part), they prefer just "Taiwan". Most of my friends don't mind at all whether you call it "China Taiwan" or "Taiwan China" or "Taipei” or just "Taiwan". We just call it Taiwan.
So I don't agree with the accepted answer from Retired Codger saying "Taiwan is a VERY sensitive subject for China". I assume he meant Mainland China there and I would correct that statement by it is very sensitive subject for the governments of both sides, for the party of mainland China and the party controlled media. But ordinary people on the mainland, I dare to say no many care! I do not care. OK I will agree that "wumao" cares if you know what that means.
I think @Malisbad's answer is more accurate and relevant " It's not a problem unless you, or they, want to make it a problem... Just call Taiwan"
One more thing, when you refer to the people, like "Chinese" or "Taiwanese" (especially say it in Chinese) it could be sensitive sometime. I know some "Taiwanese" don't like to be called "Chinese" while for our mainland Chinese, even though we don't mind just call the place "Taiwan" but if you don't think you are "Chinese" we will be angry.
I consider myself quite open minded regarding this issue. But I am quite angry when I see Taiwanese (and Hong kong people sometime) think they are "superior" to us. I just don't understand where does that sense of superiority come from.
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For the downvoter if you rather trust the answer from outsiders instead of the native, fine. I don't mind either.
From the comments I got I did realize that because you can not tell whether people are from Taiwan or Mainland and you can not tell whether they care or not you better err on the side of caution. Almost like you should not discuss about religion if you don't know people well.
But no matter what it is safe to just call it "Taiwan". If you still want to be extremely cautious about mentioning Taiwan and Mainland China together, you can say Great China Region
Again, from my own experience when you mention Great China Region, people know you are fully aware of the situation and they know you already take cautious action, they will appreciate it.