I heard today that H.P. Lovecraft was very anti-Semitic. How much truth is there to that, and what evidence do we have of it?

Anti-Semitism was fairly widespread and accepted in the United States during Lovecraft's lifetime (1890-1937), and involved variously religious and ethnic prejudices, ignorance, stereotypes, and social, economic, and political discrimination. Lovecraft prejudices regarding Jews, while not universally held, were fairly common and typical - I'll give some examples in a moment.

It's worth noting that almost all of Lovecraft's fiction and verse is free of Jewish characters. Most of what we know regarding Lovecraft's prejudices regarding Jews comes from his letters, and to a lesser extant the memoir of his wife Sonia Haft Davis (who was ethnically Jewish), The Private Life of H. P. Lovecraft. The body of Lovecraft's surviving letters, which far outstrip his fiction in sheer volume and cover practically the whole extant of his life, give a very good sense of what his prejudices were and how they developed.

Lovecraft's antisemitic prejudices were showcased very early, and suggest an environment where such views were widely accepted. At around the age of 10 or 12, he wrote and illustrated two volumes of juvenile verse titled the Poemata Minora; the illustration for “On the Vanity of Human Ambition” is a Jewish caricature with the inscription: “HIC. HOMO. EST. AVARISSIMVS. ET. TVRPISSIMVS. IUDEVS” (“This man is a greedy and filthy Jew”); and the inscription for “On the Ruin of Rome” reads:

“ROMA.REGINA.ORBIS. TERRARVM. DECEDEBAT. CVM.ROMANI.SVCCEDEBANTVR.A. GENTIBVS. INFERIRORIBVS” (“Rome, queen of the world, declined when the Romans were succeeded by inferior peoples.”)

(Quoted from S.T. Joshi's I Am Providence 1.79) These works were inspired in large part by Lovecraft's early identification with pagan Rome, and his antipathy toward Christian doctrine (although it should be remembered that some of his recollections were given decades afterwards, and may have been influenced by much later thought, reading, and experience.)

Here it is clear that by the age of twelve, despite little contact with other races, several of Lovecraft’s ideas of race and prejudices were in place. Likewise, by 1902, Lovecraft’s explorations in science had evaporated his patience with Christianity, remarking “Close reasoning was something new in their little world of Semitic mythology.” and his mother permitted him to cease attending Sunday school. (Letters to Rheinhart Kleiner 184)

In 1904, Lovecraft's grandfather died, and he entered public high school for the first time:

Here I was confronted for the first time with cosmopolitanism. Slater Avenue School is public, but it is rather a neighbourhood affair, with most of its pupils drawn from the old families. But Hope Street is near enough to the "North End" to have considerable Jewish attendance. It was there that I formed my ineradicable aversion to the Semitic race. The Jews were brilliant in their classes—calculatingly & schemingly brilliant—but their ideals were sordid & their manners coarse. I became rather well known as an anti-Semitic before I had been at Hope Street many days. (Letters to Rheinhart Kleiner 74-75)

This was basically Lovecraft's first exposure to actual Jews outside of books - he having been educated mainly at home, in a predominantly homogenous part of Providence, Rhode Island. For their part, the teachers at Hope St. appear to have tolerated this attitude without disciplining Lovecraft. He never graduated high school, however; due to a "near-breakdown," and so never went to college. For several years he lived at home with his mother, unwilling or unable to find employment or formal education. As Europe spiraled into World War I, Lovecraft became involved with amateur journalism (a large and organized endeavor with two national-level societies, dues, elected officers, etc.)

In early 1915, Lovecraft issued his own amateur periodical, The Conservative, whose political tone was cause for a rebuttal by a Jewish amateur journalist, Charles D. Isaacson, in his own journal In A Minor Key. Lovecraft responded:

Charles D. Isaacson, the animating essence of the publication, is a character of remarkable quality. Descended from the race that produced a Mendelssohn, he is himself a musician of no ordinary talent, whilst as a man of literature he is worthy of comparison with his co-religionists Moses Mendez and Isaac D'Israeli. But the very spirituality which gives elevation to the Semitic mind partially unfits it for the consideration of tastes and trends in Aryan thought and writings, hence it is not surprising that he is a radical of the extremest sort. (The Conservative 43-44)

Isaacson accused Lovecraft of antisemitism; Lovecraft's private response to this was uncouth:

A Jew is capable of infinite nastiness when he seeks revenge, & I believe I shall have ample grounds for making this particular Israelite the hero of a spirited Dunciad. I can almost predict his line of attack. He will call me superficial, crude, barbaric in thought, imperfect in education, offensively arrogant & bigoted, filled with venomous prejudice, wanting in good taste, &c. &c. &c. [...] Peace is the ideal of a dying nation; a broken race. Isaacson belongs to a stock wholly broken & emasculated by two thousand years of cringing at the feet of Aryan masters. But I, thank the Gods, am an Aryan, & can rejoice in the glorious victory of T. Flavius Vespasianus, under whose legions the Jewish race & their capital were trodden out of national existence! I am an anti-Semitic by nature, but thought I had concealed my prejudice in my remarks concerning Isaacson. I showed him every consideration in my article, carefully saying that I attacked not the man, but the ideas. However, if Jerusalem wishes to start trouble, he will find in me a new Titus, eager to inscribe on my eagles the triumphant legend IUVDAEA CAPTA! I might here remark that my anti-Semitism is not entirely due to blind prejudice. The Jews are fundamentally Orientals, whilst the rising civilization of the world is Western—Teutonic—Anglo-Saxon. The struggle between the East & the West dates back to Marathon & Salamis, & it is the West which has ever represented progress & superior culture. The Jew is an adverse influence, since he insidiously degrades or Orientalizes our robust Aryan civilization. The intellect of the race is indisputably great, but its nature is not such that it may be safely employed in forming Western political & social ideas. Oppressive as it seems, the Jew must be muzzled. Wherefore Isaacson has reason to expect a warfare of the bitterest kind if he uses his revengeful sarcasm on me. I shall not utter the first word, but shall hold the CONSERVATIVE until the serpent strikes. Then—LET HIM BEWARE. Like old Marcus Fabius on his mission to Carthage, I come with folded toga, ready for peace or war.

• H. P. Lovecraft to Rheinhart Kleiner, 10 Aug 1915 (Letters to Rheinhart Kleiner 19)

Lot to unpack there, but the short version is that Lovecraft believed in a number of popular and academic prejudices regarding Jews. Culturally, he considered them "foreign" to Anglo-American/Teutonic/Aryan/Nordic culture, and with values that didn't accord with those he attributed to himself and his own people - and biologically, he proscribed to the scientific racialism that held Jews were a people apart.

This particular idea of a scientific explanation of race was complicated, often contradictory and arbitrary, and in the very process of being undercut by researchers like Franz Boas who showed the essential biological uniformity of human beings. Lovecraft would continue to refine the idea all his life. Amateur journalism also brought him into contact, in 1919, with his first Jewish friend, the homosexual poet Samuel Loveman:

Loveman has become reinstated in the United through me. Jew or not, I am rather proud to be his sponsor for the second advent to the Association. His poetical gifts are of the highest order, & I doubt if the amateur world can boast his superior. (Letters to Rheinhart Kleiner 119)

Loveman’s gifts as a poet almost eclipsed his ethnicity in Lovecraft’s eyes; though Loveman’s apparent ambivalence in 1918 about being called into military service, caused Lovecraft to write: “If I were Loveman I should enlist. [...] But Jews will be Jews, & I will judge neither harshly nor hastily.” (Letters to Rheinhart Kleiner 129-130) Lovecraft’s published correspondence with Loveman shows no references to anti-semitism, and there is evidence from the rest of his correspondence that Lovecraft made a deliberate attempt to avoid offending his friend.

In 1921, Lovecraft's mother died. Lovecraft continued his association with amateur journalism, however, which led eventually to his meeting with Sonia Haft Greene - a White Russian immigrant from the Ukraine who was seven years older, and ethnically Jewish. Lovecraft eloped to New York and they were married in 1924.