My criteria for what makes "a Nazi" are something like this.

1. A belief that race is an immutable genetic concept, that reproducing outside one's race is inherently wrong, and that some races are inherently superior to others; most often the superior groups are "white", while the "inferior" groups include Africans, Jews and travelling people

2. Reverence for cultural "tradition", real or imagined, with any departure from these traditions classified as "degenerate" and dangerous to society. For example, a belief that avant-garde art is immoral and without value because it doesn't root itself in what are popularly perceived to be the artistic traditions of "the west", a neat line from Greek marble statues to Wagner.

3. Hatred of diversity, seeing it as a plague that rots a society. For example, the belief that women are unfit to hold a social position outside of motherhood, that non-heterosexual sexualities are "degenerate", that allowing people from another race to exist in your race's society inevitably leads to that society's destruction, that gender as a concept is a "mental illness" because only two biological sexes exist and each biological sex has a set-in-stone role demanding a certain presentation and certain values, that societies which follow one religion must not allow followers of another religion to exist within it.

4. Heavy use of absolutism. Everything is either wholly good or wholly bad. Nothing can be a mix of good and bad, or neutral. And everything is a matter of utmost urgency. Anything that is "bad" is an existential threat to all that is "good" and must be immediately and utterly annihilated.

5. An authoritarian outlook. Anything opposed by a Nazi must be forbidden by the full force of the law. There is no space for differences of opinion, or a nuanced debate, or reviewing the facts. If they oppose something, whether it's big or small - the use of marijuana, reformative justice programs, abortion, media with female protagonists - it must be banned under pain of death.

6. Violence. To a Nazi, the use of violence isn't an escalation, but the norm. They have no qualms about beating people to death simply for espousing an opposing view, or even just for existing if some aspect of their existence offends their beliefs. Likewise, their rhetoric often alludes to the indiscriminate or nonchalant, even gleeful use of deadly force - "physical removal", "showers", etc.

7. Shameless hypocrisy. The people who say "facts not feelings" as a rebuttal are often the same people whose beliefs are motivated almost entirely by feelings, and will happily mock others for trying to use evidence in their arguments instead of simply saying "it's common sense". They will shame someone for being rude and aggressive while also calling them the N word and telling them that on "the day of the rope", they'll be among the dead.

8. Veneration of strong leaders and mocking of "weakness". Consensus-builders are seen as spineless "cucks", while people who enforce their every arbitrary whim with total force are held up as "based" exemplars of good leadership and models to be emulated. People who are comfortably being themselves in ways that aren't conventionally masculine are addressed with slurs and told to kill themselves while ignorant, bullying asshats are applauded for "rustling jimmies".

You can meet all of these criteria without being a member of a National-Socialist party, or even identifying as a Nazi, but if you do meet most or all of them, your ideology can be pretty confidently described as Nazi-like.