Why did the Klu Klux Klan, a renowned anti-Catholic organization, co-opt the capirote (the infamous pointed robes) from Catholic Spain?

The pointed hoods were not a direct co-opting of the capirote, although there is some overlap. I'm going to repost what I've written before on the origin of the Klan uniforms, ~~and will add a brief addendum on the hoods at the end.~~ and with a bit more time on my hands this afternoon, worked the addendum into the answer itself to be a bit smoother reading.

As I've written about previously, much of the symbolism we associate with the KKK was the creation of fiction, not coming to us not from the original Klan of the immediate post-Civil War era, but rather consciously adopted by the Second Klan in the early 20th century in emulation of the romanticized and ahistorical portrayal in Thomas F. Dixon, Jr.'s The Clansman: A Historical Romance of the Ku Klux Klan, which was in turn adopted as the early film epic The Birth of a Nation by D.W. Griffith.

Now, to be sure, unlike the burning cross which I discuss in the linked answer, the constuming wasn't created entirely out of whole cloth. The original Klan absolutely did dress in elaborate disguises, although there is little credence of the idea that they honestly believed doing to would cause the Freedmen they terrorized to believe them to be otherworldly. To be sure, it added to the fear, no doubt, but ascribing such simplistic superstitions gives credence to the stories passed along by the Klan themselves rather than its victims.

In part the disguises of course were simply for practical purposes, to prevent identification during the commission of their crimes. It was also performative, however, and leaned into traditions that would have been understood by the public at the time and which they hoped would influence how other white persons interpreted their actions. In her study of the First Klan, Elaine Parsons sums up their purpose in this regards thusly:

As a conquered people trying to determine how far they could reassert white Democratic political and economic control, wary that northerners would suppress any direct display of organized violence, Ku-Klux had everything to gain by encouraging northerners to read their attacks as theatrical rather than political or military. By couching their attacks within often-elaborate performances derived both from mid-nineteenth-century commercial popular culture and from the long folk tradition of “rough music” or charivari, Ku-Klux adopted a time- tested strategy of the weak. As James Scott has argued, “Actual rebels mimic carnival—they dress as women or mask themselves when breaking machinery or making political demands; their threats use the features and symbolism of carnival” to “conceal their intentions” from those in power, who delay their response while attempting to determine whether the rebels are “playing or in earnest.”

The costumes were hardly uniform, however, and while some wore white, and some wore pointed hoods, but it was hardly a standard uniform, and the costumes often diverged quite far from such a description, and could be quite elaborate, such as this mask which was used by John Campbell Van Hook, Jr., a former Confederate Colonel, which well speaks to the carnival feel that many Klansmen chose to emulate. Horns were very popular, as were fake beards and animal inspired accoutrements, and a popular sentiment expressed was that they were 'the ghosts of the Confederate dead', although it ought to again be noted this was a self-identification, and we ought not give credence to victimized African-Americans widley believing that to be the case. Similar can be said for the self-identification as 'coming from hell'.

The pointed hood, perhaps the single most dominant feature in popular imaginings, while present, was, again, only one of many variations to be found, but certainly was present and can be found in imagery and artifacts of the First Klan. The comparison with the capirote found primarily in Catholic culture is often noted, and while not the same thing, the origins here to connect, as such manner of dress can be found in Mardi Gras celebrations dating well back into the 19th century, and thus be one of the many different images that the men of the First Klan were drawing on from carnival. Lacking direct attestation though, we can only look at that as a likely, well supported speculation. It is possible that more direct exposure to the capirote and its role of humiliation in Spanish culture was known; and likewise the image of the "dunce cap" worn by unruly schoolboys, and which also carried with it tones of anti-Catholicism, might have been known as well. But these images are considerably less likely to have been the inspiration, and can likely be rejected as such, with the exposure through carnival most likely, and generally agreed upon.

As such, the Mardi Gras origins are the generally better supported and agreed upon source for their attire, including the caps. It is also worth noting that Dixon didn't quite adapt the image that we have today. The still image from Birth of a Nation doesn't show the pointed hoods we all think of, but rather a thin, narrow spike. This is taken directly from Dixon, who described that "from the top of each cap rose eighteen inches high a single spike held erect by a twisted wire". Quite similar, but not quite the same, this too is another example of the varied styles of costuming we find with the First Klan. With the rise of the Second Klan, we don't , to my awareness, have notes specifically explaining why one style was chosen over the other, but the best speculation is that they were drawing on a simplified version of the imagery chosen by Dixon and then followed by Griffith, continuing the highly positioned point, but preferring the aesthetic and ease of manufacture offered by the simple cone (or if you want to engaged in some ungrounded cynicism, it meant more cloth sold by Clarke). Both were grounded in the dress of the First Klan and drawing on the terroristic traditions of the earlier hate group that had inspired them, but it only reflected one of many ways in which they originally had dressed.

So in short, the main takeaway here as regards the First Klan is that their manner of dress should be understood as costuming. Although some bands sought uniformity, even in a single group wide diversity could be found. In comparison, the Second Klan did not dress in costumes but rather in uniforms, which the well known image of the white robes and pointed mask being the expected dress of most members. While some descriptions, and surviving examples, of dress from the First Klan resembled this, it simply wasn't all that common, and there was wide room for individuality.

In the Second Klan though, there was a strong sense of hierarchy and order that precluded such forms of self-expression, and the wearing of standardized uniforms was almost to be expected - Klan literature made dubious claims about how it made everyone equal in the brotherhood. And what better than the then current pop-culture image of the First Klan? The simple white, hooded robe - the white a symbol of the racial, sexual, and religious purity that they sought to uphold - was standard for all basic members, while higher officers were given more colorful and decorated robes as befit their rank. To be sure, there is also the amusing fact behind the whole matter, namely that it wasn't just that everyone had to dress the same, but they had to dress exactly the same, with the robes manufactured by Edward Young Clarke, a early leader of the group, and sold at significant mark-up for a hefty profit.

This is the point where the popular image of the Klansmen comes into full form. Dixon's description of the First Klan had had little grounding in reality, giving them a clean, uniform look that not only didn't reflect their appearance, but contradicted how they wanted to appear, but did carry with it a strong romantic bent for nostalgic racists. The clearest example here perhaps is the pointed hood, although in The Clansman, Dixon's description is slightly different, writing that "from the top of each cap rose eighteen inches high a single spike held erect by a twisted wire". This was followed in stage productions, and would also be the style used by Griffith in The Birth of a Nation. With the formation of the Second Klan, Simmons was quite consciously echoing these depictions in the design of the uniform, and the pointed tops were something that he clearly had to incorporate as such, but exactly why he chose the slight variation isn't recorded. He perhaps prefered the aesthetic of the wider cone to the sharper point, but at the very least it is agreed he likely had the mass manufacture of the uniforms in mind, with the cones made of stiffened buckram being easier to produce en masse than the twisted wire spikes of Dixon's epic.

Both ideas did have some grounding in the First Klan, and examples can be found, but the uniformity in both cases was entirely a creation of the 20th century. Still though, while quite different in application and inspiration, the hidden identity and costuming still carried with in a performative aspect as it had with the First, but also in a much more constrained and controlled manner. An exoticism, but only to a limit.