A right wing extremist would technically be more like someone who destroys traffic lights and stop signs. The political left believes in the idea of government and authority, the right wants to be left alone.
Maybe there are cultural differences between Europe and the US. "Right extremists" might be simply different here. In most European countries, right extremists call for a strong (nationalist) state and authoritarian structures, while left extremists are closer to anarchists.
Here, right extremists set fire on refugee accommodations and are rude to, thrash or even murder foreign-looking people as well as homeless people. Their enemies are the strangers and the weak people.
Left extremists set fire on cars and other perceived status symbols of richness, and try to fight with the police. Their enemy is the capitalism in general and the state in particular.
The left extremists also did kill people, but mostly in the 1970s (see RAF [1]), while the right extremists kill lots of people all the time (see NSU [2] for a recent example).
You're talking about libertarians. There are also right-wingers who are authoritarians. Those are the ones who are more of a problem at the moment, and the ones that have, to put it mildly, historically been more of a problem in Germany.
