You’re not even using horseshoe theory correctly, not that it especially matters because it’s a horseshit theory.
Horseshoe theory is a liberal theory that equivalates socialism and fascism. But socialism is outside the Overton window of contemporary Western politics, so the theory doesn’t even apply.
In any case, liberalism and fascism have more in common with each other than with socialism. Socialism is about abolishing private ownership of the means of production, while liberalism and fascism are about the state protecting private ownership through its monopoly on violence.