In the former Soviet Union, for example, these people tend to support some variant of the old Communist Party. Their herd characteristics make for better followers than leaders. Egoist rationalists will support whatever political position, if any, they see as the most convenient for them. This will not necessarily be the same position they claim to support. But their very self-interest means that they are usually quite moderate, people one can deal with.
Altruist rationalists seek the common good, probably along utilitarian lines.
They may be very coherent and principled, but have a much more open attitude towards reality than other types. Experience does mean something to them. Usually they support some version of libertarianism, liberalism or democratic socialism. The fundamentalist mind-set may support almost any idea, provided it is taken to extremes. Islam and Marxism are typical of ideas created by fundamentalists.