Reactionary is a word which describes the politics of the far right. It’s a reaction against social progress or against the movements pushing for social progress. Fascism is a reaction against socialism and communism, it’s the current ruling class (these days, the bourgeoisie, but also in the past the aristocracy and monarchs) reacting with violence and repression against the social movements that want to overthrow them or put limits on their power and take power for the working class.

Nothing wrong with learning. Sadly, it's fairly common, with DSBM or something like that used to denote the nazi black metal artists. Outside of black metal it's generally less common, but last I heard the Epica vocalist really hates black people. Sabaton doesn't look too pretty either, being pro-Isreal and singing songs on nazi commanders and templars and shit. Don't let that stop you from being a metalhead though. There's good-hearted bands and good-hearted metalheads out there.