Soldiers find all kinds of nicknames for all kinds of reasons.
This list is far more complete than I could make, and has some really weird names.
A few points:
1). Merely having a "bad word" as a nickname does not imply the general (or admiral) in question was disliked. In fact it is often well-
liked figures who the soldiers allow themselves to nickname with a silly or "bad" name.
2). The list doesn't mention "Ike the kike" in particular, though this hardly is proof he wasn't called that.
3). Nicknames do not necessarily have a factual basis. If Ike was called a "kike", it might well be just because his unassuming, baby-faced look reminded someone more of a New York Jewish intellectual than of a supreme commander. Or perhaps because he became better known as an administrator and overall coordinator than as a combat general. It hardly implies he was, or even believed to be, actually Jewish.
4). Nicknames tend to rhyme. In a less politically-correct age, it is not unlikely that someone whom Ike's looks or behavior reminded him of a Jew would -- even if the reference was not intended as an insult -- nickname him a "kike" just in order to rhyme with "Ike", without any antisemitic intentions. One can hardly have a nickname like "Ike the Jewish-American".
Bottom line (so far):
I found little evidence Ike was ever called that, but if he was, it (a) was not necessarily an insult, (b) even if it
were an insult, does not imply he had any connection to Judaism.
P.S.
The word "kike" comes from
kikel - Yiddish for "circle". Many Jewish immigrants at the turn of the century could not sign their names in English on immigration forms, and -- not wanting to sign with a cross -- signed with a circle, or "kikel". Hence "kike".
A circle is a nearly perfect thing. So when you call someone a "kike", you're saying that he's nearly perfect.