How was Rorschach's journal translated into white supremacy?

What part of the journal made this transition in misinterpretation?

It has less to do with the journal itself, and more to do with the publisher of Rorshach's journal, the New Frontiersman, being a right-wing, racist publication. This appealed to like-minded people.

Quoting documents from Peteypedia, which elaborates further. Peteypedia is an HBO website that contains supplementary material for the show. In-universe, it contains files collated by Dale Petey, the FBI agent who was selected by Laurie Blake to be her partner when she was tasked to investigate Judd Crawford's death.

In File 1, Memo: "Rorshach's Journal":

Note: Kovacs here is "Walter Kovacs" AKA "Rorshach."

Kovacs was also an avid reader of New Frontiersman, an extreme right-tilt tabloid prone to yellow journalism and Red Scare paranoia, whose editor of the period, Hector Godfrey, was a vociferous supporter of masked vigilantes. It appears Kovacs read the newspaper to the exclusion of any other source of news. A generous appraisal of Kovacs would say that he merely collected the periodical for its glowing coverage of his war on crime. But Godfrey was also a hideous racist. An example can be found in an editorial published prior to Kovacs’ disappearance. Taking exception to a critic of masked vigilantes (until then, a largely white male phenomenon) who compared them to a modern day Ku Klux Klan, Godfrey proceeded to defend the KKK: “[I] might point out that despite what some might view to be their later excesses, the Klan originally came into being because decent people had perfectly reasonable fears for the safety of their persons and belongings when forced into proximity with people from a culture far less morally advanced. No, the Klan were not strictly legal, but they did work voluntarily to preserve American culture in areas where there were very real dangers of that culture being overrun and mongrelized.”

These psychological details, ideological frames, and media habits are incidental to an incisive understanding of Kovacs. But they are essential to any reckoning of Rorschach’s appeal and the writings attributed to him.

...New Frontiersman published “Rorschach’s Journal” in its entirety. The bookazine became a best-seller that appealed to a wide variety of curiosities, including right wing extremists. Some take it as a history book, others, devotional literature. For them, “Rorschach’s Journal”—and Godfrey’s interpretation of it—challenges the new, heretical orthodoxy that makes them feel marginalized and obsolete, written by a revolutionary they revere as a saint.

...This belief is the justification for any number of anti-social behaviors, from the formation of drop-out communities known as “Nixonvilles,” to domestic terrorists like the aforementioned Seventh Kavalry, who protest the president by committing violence against symbols of the executive branch, which is to say, law enforcement.

In File 2, Memo: Masked Vigilantes in Pop Culture

New on the radar is the re-release of The Book of Rorschach by Sons of Pale Horse, a short-lived space rock band of the nineties named after the popular death metal group that perished on November 2 during the Dimensional Incursion Event.

... all you need to know is that the album was inspired by “Rorschach’s Journal” ... and that the record is known to be popular with two types of vigilante profiles on the Werthem Spectrum, the rare Objectivist/Messianic and the increasingly common Paramilitary/Nihilist. An obvious example would be the Seventh Kavalry in Oklahoma. Field reports from Tulsa have indicated that original editions of The Book of Rorschach were found in 7K homes during the police raids that followed the “White Night” in 2016.

The record contains an essay written by Seymour David. If you know the lore behind “Rorschach’s Journal,” then you know that David was the one who discovered it while working as an editorial assistant at New Frontiersman in the eighties...

...the legends of Rorschach have inspired copycats over the decades — including those, like the 7K, who misappropriate him to some degree by projecting their own extremist ideologies onto him...