The fantasy-story of right-wing anarchy is creating misinformation, someone thinks that something like “anarcho-capitalism” is real philosophy, instead of the linguistic distortion of fascist-capitalism that it is.
Should people even specify that they are left-wing anarchists now? Do we really want to put a stop to this propagandistic joke? Anarchy will always be the extreme left into the political pendulum.
And I will tell you more: anarchism is by its nature also pacifism, as it aims to prevent any form of uncontrolled power on others. This is to silence even centrists: another fake group, people who think that it’s not “extremist” in its own abstinence, in delegating violence.
There are definitely “right-wing” anarchist currents that are popular and not as unhinged as how “anarcho-capitalism” is generally characterized, as in, anarchism that espouses the use of capitalism, but I have not really seen any genuinely “socially conservative”, anarchists. Pacifism is reactionary and emboldens the status quo.