Just like there are different kinds of Christianity there are different kinds of Islam. Some are more compatible with liberalism than others. It also depends on what you call liberalism. In the US, Republicans are thought of as Conservatives and Democrats are thought of as Liberals. However, in Europe both our Democrats and our Republicans are conservative. By the standards of the middle east, both are liberal.
Much of the conflict between the US and the Middle East stems from American foreign policy and is not because Islam and Liberalism are incompatible. For instance, the US helped to establish the nation of Israel in the late 1940's, supports Israel in all its conflicts, and is unmoved by the plight of the Palestinians. The US overthrew the Democratic Government of Iran in the 1950's to stop the Iranians from nationalizing their oil fields. The US then set up a pro-western dictator called the Shaw so the US could get lots of cheap oil. In the 1970's, the Shaw was overthrown and the present Anti-American government of Iran came to power. In the 1980's, the US allied with Saddam Hussein and sold him the weapons he used against the Kurds.
I have to be honest I dont know much about Islam but for most people religion has a lot to do with were they stand politically. why put a label on your self politically its ok to like a little of what everyone is saying. just vote for the guy you think is feeding you less B.S. With that being said you shouldn't let anyone come between you and whoever you call god. i suggest speaking with your religious leader and getting there thoughts on the matter.