Since you’re citing the ADL, can you post some links on their website to violent Left-wing organizations?
Oh and to answer your question: neo-nazis are ok when they aren’t really neo-nazis. What are the official beliefs of the purported “neo-nazis” on the ADL site you linked? Are they just a bunch of young punks who hate the BLM movement and are trying to piss people off?
They are nazis. The same type in Ukraine. They wear the black sun logo. Here’s more on their flag
The symbols for anti-Communism and anti-Capitalism are modelled after the prohibition signs: white circular field, with red border and diagonal stripe conjoined and a black symbol, hammer and sickle for anti-Communism and a bag of money (identified as such by a white dollar sign) for anti-Capitalism [5].
The NSC is also known to use other flags with “generic” neo-Nazi symbols, such as the Black Sun, which appeared in black color on white flag carried at a rally in Boston on 2020-06-27 [6, 7, 8]. The members of NSC can be identified by white badges bearing their logo in black, the same as shown on a large photo of their complex flag [5] along with other smaller objects which bear their symbols; its position might mislead the observer that it is actually a charge on the flag, but its orientation and apparent oval shape reveal that it is actually a distinctive object.
https://www.crwflags.com/fotw/flags/us%7Dnsc.html