You can be both a fascist and a socialist. A fascist can use socialist economics to reach some fascist ideas, such as National Glory, restoration of culture, or maintaining social order to prevent liberal social decay.
There are socialists that support a state, like myself. And then there are socialists that advocate anarchy, like some of the people on RevLeft. But a lot of socialists that support a fascist political system don't label themselves right wing, they label themselves Third Position.