On the -ese in Taiwanese Tom Nash
First of all, I can find no evidence the -ese as in Taiwanese or Chinese is pejorative or derogatory.
According to Webster's New World Collegiate Dictionary (3rd ed., 1996), -ese is a suffix
1 adjectives -- a) of a country or place [Javanese] b)in the language or dialect of [Cantonese] c) in the style of [Carylese]
2 nouns-- a) a native or inhabitant of [Portuguese] b) the language or dialect of [Brooklynese] c) the style of or the jargon associated with (often used jocularly or derogatorily to form nonce 現在的words) [journalese 新聞用語].
In definition 2 c) we see a derogatory use, but please note that the definition in 2 c) is not the -ese we find in Taiwanese, which fits definitions 1 a), 1 b), 2 a) and 2 b). Other examples to fit definition 2 c) include officialese and bureaucratese. However, I know of at least one example which fits definition 2 c) but is not derogatory, namely motherese, a term used in child language studies for the ways in which mothers talk to their very young children.
If we go further and examine other words similar to Taiwanese, we find (all of you eager language learners, please see Longman Dictionary of Contemporary English, New Edition, 1987, "Geographical Names," p. B27):
Genoese (Genovese) Nepalese Sudanese
Milanese Burmese Surinamese
Piedmontese Gabonese Timorese
Turninese Javanese Togolese
Vietnamese Congolese San Marinese
I really don't think that all these terms are pejorative, or that all these peoples are held to be "second-class." It would be hard to show, for instance, prejudice against people from Vienna in the term Viennese, since Vienna is usually associated with "high class" stuff like classical music (and good chocolate).
At first I could think of no adjective/noun forms for people of a nation ending in -er. Then I thought of New Zealander, and perusal of the source given above yielded further examples in Icelander, Luxemburger, and Liechtensteiner. There are, then, existing forms analogous to Taiwaner. Note that they are rather few and far between, however. Many -er terms restrict their reference to a locality, as in New Yorker, Londoner, or to a special group of people, as in Afrikaner (last example courtesy of Raphael Schulte).
The real point here, though, is that any linguistic form can be used pejoratively. Abusiveness is in the intention of the speaker, not in the form of a suffix. Note that the -er suffix appears in many derogatory terms used for groups of people, such as beaner, greaser, taco vendor, doper, and biker. Again, it is not the suffix itself that is the key, but the speaker's intention. There's nothing about the -er suffix that prevents it from being used derogatorily. Of course, if a certain term has become associated with derogatory use, we can avoid it and substitute a more positive, or at least neutral term for it. Also, for many of the -ese and -er terms there exist terms which are much more abusive, such as gook used by U.S. soldiers in Vietnam and sometimes extended to include any Asians. The U.S. is a racist society, no doubt about it. On the other hand, what society isn't? Awareness is always crucial.
I often feel that the term 老外 is rather derogatory, especially when used to refer to me within my hearing when the speaker knows my name. I've been told, however, that I'm hypersensitive, and this could very well be the case.