"Lessee. How are things consistent? Bush touts freedom, democracy and free enterprise. Says he wants those things for the oppressed people of the world. "

That's correct.

"Taiwan is a democracy which a communist dictatorship wants to overrun. "

It might want to overrun Tiawan, but the US has agreed to defend Tiawan against a Chinese attack.

"Iraq was a brutal dictatorship. Bush vowed to make it free."

Right.

"Taiwan wants to stay democratic."

And is free to do so.

"Iraq doesn't seem keen on the idea of American-style democracy."

Whatever. Unlike you, I don't wish to speak for Iraq.

"Taiwan is capitalistic, and trying to avoid a communist government."

Taiwan has relations with China. Btw, another name for Taiwan is the Repubic of China whereas China is also known as the People's Repubic of China.
http://www.gio.gov.tw/
http://www.china-embassy.org/eng/
The last link you will find mention of the "one-China policy":

"Bush told Wu that there is no change in the position he stated about the Taiwan issue when he met with Chinese Premier Wen Jiabaoin the Oval Office of the White House on Dec. 9 last year.

"We oppose any unilateral decision by either China or Taiwan to change the status quo, and the comments and actions made by the leader of Taiwan indicate that he may be willing to make decisions unilaterally to change the status quo, which we oppose," Bush said at a joint appearance with Wen at that time. "

"Iraq has been more socialistic."

You realize, of course, the British are socialists- particularly the Labor party which is in power and is being led by Tony Blair. It's a relative term, and I would say the US is far too socialistic. I think the word you looking for is Totalitarian.

"Taiwan wants help to stay free. In other words, Taiwan is an ideal situation and wants to stay that way."

But Taiwan's leader is the one advocating a change. If Taiwan does not want the US to protect it's current status, it is free to remove itself from American's miltary protection. We don't recognize Taiwan as independent of China. We think it's in our interest and everyone's interest that Taiwan remain as part of China. We support the idea of dialogue between China and Tiawan, we will not allow China to use force overthrow Taiwan- and China has agreed that it will not use force- so long as Taiwan does not insist on being separated from China.

"Iraq wants the US to go away. In other words, Iraq is a quagmire."

If Iraq leadership on July 1 wants the US to leave Iraq, then we will leave. As a sovereignty it can make this choice.

"The US has invaded Iraq."

Correct.

"The US tells Taiwan to make nice to the brutal communist dictatorship and not try to hard to stay democratic, capitalist or free."

We are fully supportive of Taiwan remaining free and capatalistic. We simply don't recognize Taiwan as separate independent state. Just as for example, we will avoid at almost all costs, recognizing the Kurds as a independent state. What relationship the Kurds form with the rest of Iraq is up to the Kurds and the rest of Iraq- as long as it's not independency we probably won't have any problems with it.

"And where's the consistency? I really don't see it."

The status of Sovereignty is based on agreements between nations, US is free to chose what kinds of agreements it adopts. Taiwan's relationship with the US is fairly unique. We recognized Taiwan as the govt of China. We just happen to recognize two goverments of China:) It is up to these two govts to resolve their differences- it's an internal matter. We have intruded on China affairs to the extent that we insist that this be resolved peacefully. But since China has agreed to resolving it peaceful, we *really* haven't intruded, except that we won't allow them to change their mind about it being a peaceful resolution. Or:
".....The KMT government, with the forces it could salvage, sought refuge on the island of Taiwan. Until his death in 1975, Chiang Kai-shek continued to claim that his government in Taiwan was the legitimate government of all of China. Meanwhile, on October 1, 1949, Mao Zedong, as chairman of the CCP, proclaimed the establishment of the People’s Republic of China (PRC) in Beijing"
© 1993-2003 Microsoft Corporation. All rights reserved.
From Microsoft Encarta

More from Encarta:
"In 1917 China entered World War I on the side of the Allies (which included Britain, France, and the United States) in order to gain a seat at the peace table, hoping for a new chance to halt Japanese ambitions. China expected that the United States, with its Open Door Policy and commitment to the self-determination of all peoples, would offer its support. However, as part of the negotiation process at the peace conference in Versailles, France, U.S. president Woodrow Wilson withdrew U.S. support for China on the Shandong issue. The indignant Chinese delegation refused to sign the Treaty of Versailles.

Young people in China who looked to the West for political ideals were crushed by the decisions at Versailles. When news of the peace conference reached China on May 4, 1919, more than 3,000 students from Beijing universities assembled in the city to protest. The Beijing governor suppressed the demonstrators and arrested the student leaders, but these actions set off a wave of protests around the country in support of the Beijing students and their cause (see May Fourth Movement)."

© 1993-2003 Microsoft Corporation. All rights reserved.

That's what happens when you elect a Dem as the President:)