There's really no way to be politically neutral on this unless you choose to exclude both China and Taiwan from your site. If you don't want to offend the Chinese visitors, then you'll need to represent Taiwan as a province of China. If you don't want to offend the Taiwanese visitors, then you need to represent Taiwan as an independent state.
However, there are some Taiwanese citizens who believe that Taiwan is China, and that the Taiwanese government is the legitimate government of China. This is why the Chinese embassy in the U.S. is actually the Taiwanese embassy (pissing off a lot of Chinese people). This is also initially why Taiwan had been denied admission into the U.N. for the past 40 years—because the KMT party which had governed Taiwan under a military dictatorship for most of Taiwan's history refused to call itself anything but the "Republic of China", despite being expelled from China decades ago as well as the Chinese seat in the U.N. having been passed to the communist government that now ruled the People's Republic of China. After all, there couldn't be 2 "Chinas" in the U.N.
At this point, even if Taiwan wanted to enter the U.N. as "Taiwan", which I believe the former president wanted to do, they would probably be prevented from doing so as China has gained a lot of economic and thus political clout over the past decade. So the ISO standard is unlikely to change on this point.
So on the one hand, you have the ISO standards, which are based on U.N. dogma, and on the other hand, you have reality: Taiwan/RoC and China/PRC have been separate political entities for as long as either has existed. The Dutch and Portuguese had at some point established bases on the island in the 16th and 17th century. And when the Ming dynasty ended, some loyalists fled to Taiwan to establish the Kingdom of Tungning, and the same thing basically happened with the KMT when they were kicked out of China by the communists. But no government has ever held control in both regions simultaneously.
To date, Chinese law has never been enforced in Taiwan or vice-versa. The government in Taipei has also never collected a single cent of tax from China, and likewise Beijing has never collected taxes from Taiwan. Those are the political realities. But another political reality is that a Taiwanese passport says "Republic of China" on it, not "Taiwan". (Edit: During the DPP administration from 2000 to 2008, the first time a non-KMT president was elected in Taiwan, the word "Taiwan" began replacing "China" in the names of government-owned enterprises, and "Taiwan" was added below "Republic of China" on embassy signs. Protective covers which simply read "Taiwan Passport" were also issued for Taiwanese passport holders. Ironically, the U.S. government condemned these actions in order to show their support for the PRC's One-China policy, while at the same time Taiwanese passport holders have historically and continue to be hassled by U.S. customs agents for having "China" on their passports.)
IMO, the practical thing to do is just add a separate country code for Taiwan for the Taiwanese users who consider themselves Taiwanese (which is still most). I mean, we break standards all the time. After all, how many of our web pages validate perfectly? Unless your site uses ISO country codes for some sort of interoperability with 3rd party apps, this is another case where blindly following standards serves no purpose. And even though your Chinese visitors may scoff at the Taiwan option, they're unlikely to be upset by it enough to stop using your site.
Put another way, would you force your Palestinian users to call themselves Israeli just to appease non-Palestinians? Or would you ever force your Japanese users to call themselves Chinese just because of an ISO standard? We jump through all sorts of hoops to let users use any browser they want, so why not make this minor concession to let Taiwanese users call themselves Taiwanese?