The Spanish scholar on the Black Legend, Ricardo Garcia Carcel, has an authoritative book on the subject (La Legenda Negra). He makes a bunch of really good points about how to understand the Black Legend.

"It is neither a legend, insofar as the negative opinions of Spain have genuine historical foundations, nor is it black, as the tone was never consistent nor uniform. Gray abounds, but the color of these opinions was always viewed in contrast [to what] we have called the white legend." (14)

My area of specialty includes the Dutch Revolt. Important pieces of propaganda that have contributed to what has been deemed the "Black Legend" came out of this eighty year conflict. If one looks at the personal correspondences of individuals such as the Duke of Alba, or at the atrocities committed by the arrears-owed Spanish Army against civilians during the "Furies," it is clear that the brutality exhibited by the Spanish in Black Legend materials has legitimate, real origins.

However, an important part of the black legend is that the propaganda campaign has had some sort of coordination. Not necessarily between individuals, but moreso in form. The idea was that the brutality of the Spanish was inherent to their "spaniard-ness." This idea would become subsumed under conceptions of race that came about later on. Thus, the racist element.

This second part has been shown, in La Legenda, to be non-existent. Simply put, there is no over-arching "Black Legend" to which all of the negative connections that have been foisted upon brown people and latino people can be attached. There is no "Black Legend" mass of propaganda initiative aimed at perpetuating racist historical narratives or historiographies.

The Spanish were one of the more brutal colonial powers. By the time the Dutch were revolting, Spain had already engaged in the horrific atrocities outlined the De Las Casas accounts. In fact, one of the most famous and prestigious scholars of Spain, Francisco di Vittoria, had already made arguments against the justifications for treating indigenous peoples with brutality and subjugation.

Now, one of the other things mentioned by Carcel is the "White Legend." This is essentially Holocaust denial/colonialism apologia/chauvinism/jingoism/etc. type "washing" of history. As you mentioned, the far-right love the White Legend. They try to erase or sanitize the atrocities of the Spanish past. This version is actually coordinated. As such, we as historians must always look at the Black Legend while giving consideration to its relation to the White Legend.
On top of that, sometimes parts of a historical project are accurate and "good" history writing and research, and sometimes parts aren't. If I wrote a history or Spain and left out parts of their atrocities, not on purpose but still an important omission, yet still included quotes from perhaps a discriminatory source on Spanish culture, what type of "legend" would you say that conforms to? It's got parts of both, so is the distinction so easy to make? Not really.

I would say, as an historian, it's important that you remember to look at all claims independently, and make sure to pay attention to the argument being made with respect to how it portrays atrocities, subjugation, colonialism, or oppression in ways that you recognize. If you see a piece denigrating some part of Spanish history or culture, are the reasons easy to understand? Couched in weird terminology? Aimed at a particular group? Once you find out, try and see how they frame these events. Necessary? Tragic? Triumphantly? The White Legend employs all of the manipulative tactics that one uses to make an argument convincing, even if it is invalid or untrue.
The Black Legend tends to be more of a nebulous formation of historiographical shortcomings by historians. Whether those be intentional, personal biases towards the content, or widespread, negative conceptions of groups of people and cultures, is not so clear. What is clear is that these shortcomings aren't coordinated, and they aren't some tradition that is passed down.

History being written by the victors is an awful and inaccurate over-simplification of how history actually works as a tradition. However, it is a good tool to understand how to view the Black Legend. The Spanish were a colonial power. They hurt a lot of people and fought a lot of people. They had enemies that made propaganda about them, just as they made propaganda about themselves and their enemies. Now, if you take the aggregate of all of the writing about Spanish history, there is that huge period where they were hurting people all over the world. If you look at that pile of writings, you will find a whole spectrum of feelings and discourse about the Spanish. Seeing as how they were a brutal colonial power, there is going to be a LOT of that pile that has harsh words about the Spanish. Yet, all of these accounts aren't coordinated against the Spanish as a people, but moreso a reaction to the oppression of a subjugating power. Thus, you get trends and memes and things that occur throughout that pile of negative accounts. The lack of coordination is key though. The White Legend is an actual, pointed goal of erasing the atrocities of the Spanish past. Thus, it is definite in it's scope and form.

This is a subject requiring incredible nuance and touch, because there is quite a bit of everything.

There has been quite a notorious "Black Legend", which is a general concept more commonly associated with Julián Juderías' book of the same title, and in recent years with Elvira Roca Barea's book "Imperiofobia y leyenda negra". So, what is the Black Legend?

The Black Legend was the constant flow of propaganda against anything Spanish that started from around the time the Spanish kingdoms began to become forces to be reckoned with. The start of the "black legend", and I am going to keep using that blanket term for it is short and catchy, can be pinpointed to Italy in the very late 15th century. In that time, king Ferdinand II of Aragon (more commonly known as the male half of the Catholic Monarchs) took over the Southern half of Italy, and the Spanish influence in the papacy was immense. The pope was also Spanish, and started owing favours to Ferdinand, which is as mentally comforting as owing a big fat one to Vito Corleone.

Pope Alexander VI, also known as Rodrigo Borgia, was the head of the famous Borgia (or Borja) family. He was subject to a full campaign of defamation and slander from the Italian noble families, most notably the roman patricians like the Colonnas, Orsinis, and others of that same ilk. He was accused of anything you can think of: murder, conspiracies, sacrilege, formidable orgies at the Vatican, incest with his own daughter who was also accused of sleeping with her brother, the whole lot. The Borgias were no saints (except for Saint Francis of Borja but that comes a century later) but were no monsters either, and were definitely par for the course for Italian lordly families of the time like the Medicis, Viscontis, Sforzas, Colonnas, Caetanis, or Farneses. The main difference between the Borgias and the rest is that they were foreigners, intruders into the papacy, which was basically a highly lucrative business for the Italian families, and they were not going to let a Spaniard take over their whole operation. This is the first great landmark of the Black Legend, but it gets much bigger when religion gets into the fray.

In the mid 16th century, king Philip II inherited the Spanish crowns and also the Burgundian possessions: Franche Comté, Burgundy, and the Northern and Southern Low Countries. It was the time of the Reformation, and the Northern Low Countries were heavily packed with reformists, and the Southern Low Countries were not exactly devoid of protestantism (kind regards to my greatly admired Francisco de Enzinas, a disciple of Melanchthon). When rebellion erupted in 1568, the religious divide was painfully obvious: the more Catholic a zone was, the more likely it was to be loyal to the King of Spain; the more protestant it was, the likelier to take arms for the rebels.

Spain tried to quell the rebellion the ordinary way rebellions are suppressed: the army. The Spanish armies, which were quite multi-national by the way, were very often underpaid, paid late, or not paid at all, which would normally result in mutinies and abuses by the army against the peoples, extorting food, water, wine, cash, or whatever supplies they needed. This is par for the course for the time as well, not something exclusively Spanish. The Duke of Alba's ferocity and brutality, hanging over a thousand prisoners, became proverbial, with pictures, paintings, sketches, and cartoons popping here and there showing him as a monster who ate babies, protestants, and generally enjoying the anthropophagic diet (something any sane dietitian would not recommend). Spain's long war in the Netherlands led to many abuses, and some of them left an indelible mark on the Northern and Southern Low Countries, like the Pillage of Antwerp (Saco de Amberes, Sac d'Anvers).

The Spanish army abuses were not exclusive to the European continent, the level of attrocities commited by some Spanish soldiers and officers is bone-chilling, and I am specifically thinking of García Hurtado de Mendoza when he was Captain General of Chile. When his juicio de residencia came, he was found guilty of 198 charges, was disallowed from holding any sort of offices in America for 20 years, and was fined 6 million reales.

Attrocities did happen, and there is no point in denying them or justifying them. Probably my friend u/aquatermain or u/drylaw can give a few accounts. But then comes the question of the propaganda campaigns coming from France, England, and the Netherlands. The propaganda efforts are absolutely real and clearly documented, but we also have to consider that Spain was frequently at war with any combination of those three territories, and war-time propaganda is the usual state of affairs.

King Philip II had quite a tragic personal life. Among other things, his firstborn son, prince Charles, was definitely insane. His insanity led to paranoid delirium and eventually to conspiring against his own father, who had no other choice but to imprison him. The tragic story of prince Charles fuelled the imagination of countless authors, all of them blaming his father for whatever devious shit their minds could concoct. This black legend of King Philip II and prince Charles lasted until well into the 19th century, when Verdi composed his opera "Don Carlo". Philip II was called in the Netherlands "the Black devil of the South", a title that gives name to a famous book by Ricardo García Cárcel from 2017 where he analyses all of the propaganda, smears, and slanders thrown at king Philip.

I would frankly recommend reading "La leyenda negra" by Julián Juderías, and "El demonio negro del Sur" by Ricardo García Cárcel to have a solid grasp of the Black Legend, as they are very accessible books by writing style and general availability on AbeBooks, Iberlibro, Amazon, local libraries, etc