I interpret the sentence as meaning, “the Apaches are so frightening that they would give even a watermelon a feeling of intense fear.” Elrod’s grin and the man’s reaction suggest that the sentence is meant sarcastically.
The watermelon has long been a stereotypical crop of the Southern United States, and the phrase “pure fit” (meaning “intense feeling or outburst of emotion”) came in the 1970s and 1980s to be used as a stereotypical Southern dialect expression in Western novels and Western-set historical romances. By combining these elements into one sentence of dialogue, Cormac McCarthy gave his character a double dose, as it were, of Southernness.
The phrase “pure fit” is a straightforward composition of these senses of the words:
pure, adj. 3.b. Used emphatically or as an intensifier: nothing but (the thing specified); sheer, utter, complete, total, unmitigated.
fit, n.2 4.f. A violent access or outburst of laughter, tears, rage, etc.
Oxford English Dictionary
With an appended description of the type of emotion, the phrase appeared in the late 19th and early 20th century in England: one could have “a pure fit of tenderness” (1895), “a pure fit of freakish obstinacy” (1912), “a pure fit of nerves” (1914), “a pure fit of experimentalism” (1920) and so on.
Without an appended description, the phrase appears in the 1960s in the United States. Here’s the earliest instance I could find:
It was a glorious defensive job […] all 11 were in a pure fit to get at Simpson.
Dan Jenkins (1968). ‘The Day They Tied Up O. J.’. Sports Illustrated, 9 December 1968, p. 21.
Other early instances of the phrase appear in dialogue by characters from the Southern United States, in historical settings from the mid 19th to early 20th century:
“Ain’t it strange them dogs o’ yourn never tuk no notice atall of a common man sich as that fust preacher we had, an’ then they went an’ pitched sich a pure fit over this here high-minded feller?” […] “Then the fust airplane that come—they pitched a pure fit over hit.”
Louise Howe Bailey (1974). Go Home Wi’ Me, pp. 79–80. Groves. Setting: North Carolina, early 20th century.
“He ain’t gonna like it. Not one bit. He’s gonna have a pure fit. Ain’t no stableboy ever set his boots under his table before.”
Patricia Hagan (1981). Passion’s Fury, p. 47. New York: Avon. Setting: Alabama, mid 19th century.
“It’s just that I’ve never danced with a gunfighter before. My father, bless him, would have a pure fit, if he saw me dancing with you.” She wrinkled her nose. “To be truthful papa has a pure fit if he sees me dancing with most anybody.”
Linda Benjamin (1982). Ecstasy’s Fury, p. 336. New York: Kensington. Setting: New Mexico, mid 19th century.
“Well, I heard little Loma threw a pure fit down at the store today,” said somebody else. “You want my opinion, Rucker’s been hopin’ to git shet a-Mattie Lou ever since he laid eyes on the milliner.”
Olive Ann Burns (1984). Cold Sassy Tree, p. 88. New York: Dell. Setting: Georgia, early 20th century.
“Big tells ’em, way I hear it. Whipped three at the creek crossin’ and tied ’em across saddles to trot home. Ol’ Clifton like to throwed a pure fit.”
Lee Raintree (1985). This Promised Earth, p. 175. New York: Bantam. Setting: Alabama, mid 19th century.
So by the time Cormac McCarthy was writing Blood Meridian (1985), set in Texas and Mexico in the mid 19th century, “a pure fit” was a stereotypical expression for his setting, despite there being no contemporary written evidence that the phrase was used in that place and period.