“Hate injures the hater, not the hated” has usually been credited to Peace Pilgrim (1908-1981), who was born Mildred Lisette Norman. However, Peace Pilgrim clearly indicated that the saying was an old one:
 
“There’s something to that old saying that hate injures the hater, not the hated.”
 
“Hate can work great harm, It Is true, but only to the hater, not the hated” was cited in “Hating Hurts the Hater” by George Ross Wells in the May 27, 1936 Hartford (CT) Courant. “Hate injures the hater, too.. Hatred stirreth up strifes, but love covereth all sins.—Prov. 10:12” was printed in many newspapers in 1938.
   
 
27 May 1936, Hartford (CT) Courant, “Men and Manners: Hating Hurts the Hater” by George Ross Wells, pg. 15:
Hate can work great harm, It Is true, but only to the hater, not the hated.
 
30 August 1938, The Record-Argus (Greenville, PA), pg. 2, col. 1:
HATE INJURES THE HATER, TOO. Hatred stirreth up strifes, but love covereth all sins.—Prov. 10:12.
 
Google Books
In the University Tradition
By Alfred Whitney Griswold
New Haven, CT: Yale University Press
1957
Pg. 61:
Again and again, in life and in the great literary classics it has inspired, we see hate destroying the hater, not the hated, as it destroyed Saul in his enmity for David.
 
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Justice Party golden jubilee souvenir, 1968
Madras: Copies available with K. Paramasivam, Secretary, Justice Party
1968?
Pg. XXX:
These wise men do not realise that hate injures the hater more than it does the hated one.
 
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Up from the Ghetto
By Phillip T. Drotning and Wesley W. South
New York, NY: Cowles Book Company
1970
Pg. 146:
“Then he said, ‘Always remember that hate consumes the hater, not the hated.’”
 
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Steps Toward Inner Peace
By Peace Pilgrim
Hemet, CA: Friends of Peace Pilgrim
[between 1981 and 1996)
Pg. 10:
It is said that hate injures the hater, not the hated.
 
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Peace Pilgrim:
Her Life and Work in Her Own Words
By Peace Pilgrim
Santa Fe, NM: Ocean Tree Books
1991
Pg. 63:
There’s something to that old saying that hate injures the hater, not the hated.
 
Google Books
1,600 Quotes and Pieces of Wisdom That Just Might Help You Out When You’re Stuck in a Moment (and can’t get out of it!)
Compiled by Gary Guthrie
Lincoln, NE: iUniverse, Inc.
2003
Pg. 54:
There is something to that old saying that hate injures the hater, not the hated. —Mildred Norman Ryder, the Peace Pilgrim