The AP Style Guide shall lead the way:
A political grouping or tendency mixing racism, white nationalism, anti-Semitism and populism; a name currently embraced by some white supremacists and white nationalists to refer to themselves and their ideology, which emphasizes preserving and protecting the white race in the United States.
Avoid using the term generically and without definition, because it is not well-known globally and the term may exist primarily as a public relations device to make its supporters’ actual beliefs less clear and more acceptable to a broader audience. In AP stories discussing what the movement says about itself, the term “alt-right” (quotation marks, hyphen and lowercase) may be used in quotes or modified as in the self-described “alt-right” or so-called alt-right.
Depending on the specifics of the situation, such beliefs might be termed racist, white supremacist or neo-Nazi; be sure to describe the specifics. Whenever “alt-right” is used in a story, include a definition: an offshoot of conservatism mixing racism, white nationalism, anti-Semitism and populism, or, more simply, a white nationalist movement.
When writing on extreme groups, be precise and provide evidence to support the characterization. Report their actions, associations, history and positions to reveal their actual beliefs and philosophy, as well as how others see them.
Some related definitions:
racism The broad term for asserting racial or ethnic discrimination or superiority based solely on race, ethnic or religious origins; it can be by any group against any other group.
white nationalism A subset of racist beliefs that calls for a separate territory and/or enhanced legal rights and protections for white people. Critics accuse white nationalists of being white supremacists in disguise.
white separatism A term sometimes used as a synonym for white nationalism but differs in that it advocates a form of segregation in which races would live apart but in the same general geographic area.
white supremacy The racist belief that whites are superior to justify political, economic and social suppression of nonwhite people and other minority groups.
neo-Nazism Combines racist and white supremacist beliefs with admiration for an authoritarian, totalitarian style of government such as the German Third Reich to enforce its beliefs.
antifa Shorthand for anti-fascists, an umbrella description for the far-left-leaning militant groups that resist neo-Nazis and white supremacists at demonstrations and other events. Until the term becomes better known, include a definition in close proximity to first use of the word.
“alt-left” A term that some use to describe far-left factions. See “alt-right” for usage guidelines.
This is actually a big deal. Most news stories are written with the AP Style guide, um, guiding them, and if it has bubbled-up to their management that these stories need a consistent usage, then there is a culture shift happening (and happening rather fast). Part of this is about framing the stories, but if you look closely, most the definitions are on the bad players playing badly.