Mark Jones, 25, and Alice Cutter, 23, both of Sowerby Bridge near Halifax, West Yorkshire, deny being members of what prosecutors have called the "unapologetically racist" National Action group, between December 2016 and September 2017.
The Crown also alleges that Garry Jack, 24, from Heathland Avenue in Birmingham, and 18-year-old Connor Scothern, of Bagnall Avenue, Nottingham, are guilty of belonging to the banned organisation between the same dates.
Opening the case at Birmingham Crown Court on January 7, prosecuting barrister Barnaby Jameson QC alleged that all four were part of "a fellowship of hate", made up by some "50 or 60" hardcore activist members of National Action.
He told the jury: "We are entering the neo-Nazi world of 'White Jihad'. We are talking about a tiny, secretive group of die-hard neo-Nazis with no compunction about attaining their objectives with the use or threat of terror.
"A group with a common admiration for Hitler and the architects of the Holocaust. A group that shared the same pathological racial prejudice and conviction in brutal white supremacy. A group with a shared enthusiasm for ethnic cleansing. A group with a particular interest in the eradication of the Jews."
Police release horrifying footage of dangerous drug driver causing chaos on Yorkshire's roadsBoy, 12, who lost father and stepfather in road tragedies died after being hit by carHe added: "This is a case fuelled by hate. Those are not my words. The group arranged, as you will see, its own Hate Camp. Ultimately this is a case about a fellowship of hate. Immovable and unrepentant hate.
"A hate so fanatical and a fellowship so defiant that the accused would sooner break the terrorism laws than break their bonds of hate."
He told jurors they would be wrong to believe that the "undiluted Nazi ideology" of Germany's Second World War-era Third Reich had died with Hitler.
Mr Jameson said: "For the accused in this case, and other individuals you will hear about, Hitler's work will always be unfinished. A group for whom the 'Final Solution to the Jewish question', to use Hitler's words, remains to be answered by complete eradication."
He added: "The group in this case had an innocuous name - National Action. Their ideology was anything but innocuous. Unapologetically racist and aggressive, it was the genesis of a home-grown Nazi 'storm detachment'.
"It advocated the same Nazi aims and ideals - the violent ethnic cleansing of anyone who did not fit the Nazi mould of racial purity: Jews, primarily, but also blacks, Asians, gays and liberals. The group had particular venom towards female Labour Members of Parliament.
Convicted Hull murderer 'did not hesitate' to fight off terrorist on London BridgePhotographer interviews his mother about father’s death for poignant Sheffield exhibition"When Jo Cox MP was murdered in June 2016, one National Action member, Jack Coulson, went on social media hours after her killing to declare her killer, Tommy Mair 'an absolute legend'.
"The ultimate aim of the group was all-out race war or 'Rassenkreig'. This was not, as you will hear, a talking shop. Members of National Action were equipping themselves with weapons and the ability to produce explosives.
"In one instance you will hear a National Action member - the same Jack Coulson - constructed a pipe bomb."
Mr Jameson told the eight men and four women of the jury: "The Crown should make it clear at this early stage that this case, involving as it does Nazi fanatics, will by its nature lead you, the jury, into a world as dark as a black sun."
He added: "It is a world that will transport the court back to the horrors of Nazi Germany: the concentration camps, the gas chambers, the crematoria and the chimneys that funnelled human ash into dark skies."
Mr Jameson said: "You will be exposed to language of shocking racial hatred. You will be exposed to humour that is beyond sick. The material is not there to be gratuitous.
"It is there to give you first-hand insight into the mindset of each of the accused. The mindset, in other words, of each fanatic. The more disturbing the evidence, the more important for you, the jury, to approach it, as I know you will, with a high level of objectivity and detachment."
The accused all deny being members of a terrorist group and the Crown's opening of the case is continuing.
The trial is expected to last up to 10 weeks.