What kind of political philosophy or ideology doesn't easily fit into the right-left spectrum commonly used to characterize American politics?
I have looked every where and the only ones I can find are Islam and Fascism.
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There are actually a lot of other axis on which individuals or political powers can position themselves independently:
Should the state try to create a society where everyone is equal? Or promote a society with a clear class hierarchy? Different elitists will disagree on which members of society should be the elite. A couple examples of criteria different elitist movements promote are heredity (monarchism), personal accomplishments (meritocracy), personal wealth (capitalism), ethnicity (racism) or any other criteria one could use to legitimate a preferred position in society.
(Note that it is very rare for anyone to self-describe as an elitist. The term is mostly used to discredit political opponents who claim to be egalitarian. The accusation is usually that they use egalitarian arguments as a cover to promote one class of society over others. Actual elitists usually self-describe with a more specific terminology)
Should the state maintain control over the actions of their citizens for the benefit of everyone or let them do as they please as long as they do not violate the rights of others?
If one wants to enforce any of the political ideas listed here to a high degree, then a certain amount of state authority is almost always required. Which is the base of the horseshoe theory which says that any form of political extremism does also require a pinch of authoritarianism.
Should the state see other states and their citizens as rivals and oppose them, or as partners and cooperate with them?
How much should the state invest into maintaining its armed forces? Should the state use its military only for defending its own borders, or is it an acceptable tool for protecting other interests? Militarism does not necessarily imply nationalism, because a state can send its army to aid other states against external or internal threats (Interventionism).
Should the state promote and support one specific religion and incorporate its ideals into its decision-making or should religion be irrelevant for political decisions? (Different fundamentalists can additionally disagree on which religion to support. Some religious doctrines mandate a specific positioning on one of the other axis)
Should society oppose changes to their value system (regardless of what this system is right now) or should it be flexible in its values and be able to adapt to how external circumstances affect them? Conservativism often seems similar to Fundamentalism in many modern societies, but that's because many societies are traditionally fundamentalist. The Christian missionaries during the age of colonialism, for example, would be considered progressive by the locals, because they promoted fundamental values to societies which used to be traditionally secular.
Your example of Fascism would be elitist (of the racism flavor), authoritarian, nationalistic and militaristic. Fascists can be either fundamental or secular, depending on whether or not they base their position on a religion or not. They can be either progressive or conservative, depending on if the society used to be traditionally fascist before or if they want to turn a non-fascist society into a fascist one.