The "kill count" for Shining Path seems to be around 30,000. According to the Truth and Reconciliation Committee report which Wiki cites (and as far as I can tell, does so truthfully), that number is 31,331 killed or missing.

Now, with the Spanish Civil War, you can answer this a few ways. First, we can look at all deaths committed by the Republican forces in what was called "The Red Terror". Second, count just those by the CNT. And third, only the killings of priests and nuns, which seems to be your friends contention.

Simply put, he would only be correct on a single count. According to Antony Beevor's book on the war, the total killed in the so called Red Terror was just under 40,000. /u/Domini_canes probably can give you all of the various estimates, as they do get higher, but most histories I have read (Beevor, Thomas, Preston) don't go much higher than 50,000.

But that includes all of the leftist factions, not just the CNT. While especially in the early months the CNT were somewhat zealous in their anti-clericalism, that was not the entire Red Terror. I don't have any source that even attempts to offer a breakdown, but the Anarchists were only a small part of the overall makeup of the Loyalists, and I've never read any source that attributes the bulk of the Red Terror to the CNT. Especially in the latter part, the Communists really did their part.

Specifically in regards to clerical deaths, the most authoritative numbers are all under 10,000. This article, which Wikipedia relies on, cites 6,832 members of the clergy killed, and other sources I've read echo 6,800 as being fairly authoritative.

So anyways, the point is, that your friend is either sorely mistaken in their belief that the CNT equaled the body count of the Shining Path, or both lacks much in the way of basic knowledge about the Spanish Civil War factions and thinks that all of the victims of the Red Terror were clergy.

/u/Georgy_K_Zhukov has already cited the accepted number for anticlerical murders during the Spanish Civil War: 6,832. The article he links to relies on Montero Moreno's research, which has not been substantially challenged since he published it in the 1960's. For the overall numbers in the Red Terror I rely on the same estimates that Zhukov does, and the english language gold standard for all violence against noncombatants in Spain during the war is Paul Preston's The Spanish Holocaust. While this book focuses largely on the violence in Nationalist territory it does cover the Republican zone as well. There has been a recent (since the year 2000) burst of scholarship regarding violence against noncombatants in Spain during the war. Most of it has focused on the Nationalists, but Republican atrocities have been investigated as well. Still, the 6,832 for clergy killed in the war has not been changed.

There is a danger in overstating this particular aspect of the Spanish Civil War. The numbers suggest that anticlerical violence was a mere drop in the bucket in a veritable orgy of violence against noncombatants undertaken by both sides of the war. However, "[t]he anticlerical fury of 1936 ... was the greatest bloodletting in the entire history of the Christian Church." (Jose M. Sanchez, The Spanish Civil War as a Religious Tragedy, pg 8) With the majority of the murders taking place between one month and six months after of outbreak of the war, the violence against clerics is unprecedented at least numerically. So, while under 7,000 dead is a mere blip when viewed in the context of the Spanish Civil War's hundreds of thousands killed, it is an important moment in the context of the history of Catholicism.

The aforementioned Sanchez does a masterful job in his book in laying out the reasons why this violence occurred. While the author is Catholic himself, he readily admits the corruption that was all too common in the Church in Spain at the time. Being perceived as aligned with the state against the people was another aspect of the question. The area that Sanchez is superior to Preston is in describing the rhetoric amongst various groups on the left that inspired the violence. Preston uses the argument that it was a spontaneous outbreak of indignation, and Sanchez ably refutes that idea (particularly in pages 37-42). In the pages following that deconstruction, he describes the excesses of the violence—desecrating tombs, putting cigarettes in the mouths of disinterred corpses, playing soccer with the skull of a corpse, and more. All of this was summed up by Andrés Nin, who said that “[t}he working class has solved the problem of the Church very simply; it has not left a single one standing.” The anticlerical violence in Spain was planned, it was ongoing, and it was seen as a positive by far too many on the left. There is an argument to be made that the violence only stopped because it was being used as effective propaganda fuel by the Nationalists.

For more information on the anticlerical violence, Preston’s Holocaust is excellent but limited. Sanchez’s Religious Tragedy is outstanding, and the author’s pro-Catholic bias is remarkably mild. For example, he denounces Franco’s regime as “barbarous” and completely destroys the idea that the Spanish Civil War was some kind of “crusade.” As always, followup questions from OP and others are encouraged.