Eisenhower's don't ask, don't tell

[snopes]

Comment: Is the following true?

'In the late 1940's, future U.S. President
Dwight Eisenhower asked one of his aides, Nell "Johnnie" Phelps, to
compile a list of known lesbians in the WACS, so they can be ferreted out.
Her reply was along the lines of, "Yes, Sir, but please realize on that
list will be the names of many highly regarded and even honored clerks,
secretaries, nurses, motor pool workers, and even myself." Upon hearing
this, Eisenhower was alleged to have commented, "Forget about the list."'

This is a potentially powerful story, but based on my research, Eisenhower
and Phelps' timelines don't coincide correctly for this to be true.