The Shorter Slang Dictionary (1994) says:
hate (sb's) guts to dislike (sb) intensely. Adopted from the USA around 1937.
The New Partridge Dictionary of Slang and Unconventional English (2008) says:
guts noun 1 the stomach; the general area of the stomach and intestines. Standard English from late C14; slipped into unconventional usage early in C19 UK, 1393. 2 the essentials, the important part, the inner and real meaning UK, 1663.
hate someone's guts to hate someone intensely UK, 1918
The Historical Dictionary of American Slang has a similar "I hate his intestines" from 1901, and according to chief editor Jonathan Lighter: "Guts being regarded in that far-off age as rather vulgar."
I found a 1913 (and possibly 1912) antedating. Within The Law was a Broadway production in 1912, written by Bayard Veiller. Here's an extract from the 1913 book based on the play (plain text / full view) "by Marvin Dana from the play of Bayard Veiller":
"Was there any bad feeling between you and Eddie
Garson's reply was explicit.
"Never till that very minute. Then, I learned the
truth about what he'd framed up with you." The speaker's
voice reverted to its former fierceness in recollection,
of the treachery of one whom he had trusted.
"He was a stool-pigeon, and I hated his guts! That's
all," he concluded, with brutal candor.
The same line appears in 1917 books of the script, and I expect it was also in the original production which was first performed at Eltinge Theatre, New York, September 11th 1912.
Via ADS-L is a 1911 found by Garson O'Toole:
[ref] 1911 June 3, Seattle Daily Times, Stenographic Report of Today's Testimony, Quote Page 8, Column 6, Seattle, Washington.(GenealogyBank)[/ref]
[Begin excerpt] You further said: "I hope I may never see my mother alive if I ever gave the ---- a cent. I never had use for him, and I hate his guts." [End excerpt]
(The dashes above represent a single long dash.)