Historically it IS racist because that's how it started out
No, it didn't. From the article that you linked, under Origins:
The first record of a similar rhyme is from about 1815, when children in New York City are said to have repeated the rhyme:
Hana, man, mona, mike;
Barcelona, bona, strike;
Hare, ware, frown, vanac;
Harrico, warico, we wo, wac.
The "Hana, man" was found by Henry Carrington Bolton in the US, Ireland and Scotland in the 1880s but was unknown in England until later in the century. Bolton also found a similar rhyme in German:
Ene, tene, mone, mei,
Pastor, lone, bone, strei,
Ene, fune, herke, berke,
Wer? Wie? Wo? Was?
Variations of this rhyme, with the nonsense/counting first line have been collected since the 1820s, such as this Scottish one:
Hickery Pickery, pease scon
Where will this young man gang?
He'll go east, he'll go west,
he'll go to the crow's nest.
Hickery Pickery, Hickery Pickery
More recognizable as a variation, which even includes the 'toe' and 'olla' from Kipling's version, is:
Eenie, Meenie, Tipsy, toe;
Olla bolla Domino,
Okka, Pokka dominocha,
Hy! Pon! Tush!
This was one of many variants of "counting out rhymes" collected by Bolton in 1888.
A Cornish version collected in 1882 runs:
Ena, mena, mona, mite,
Bascalora, bora, bite,
Hugga, bucca, bau,
Eggs, butter, cheese, bread.
Stick, stock, stone dead – OUT.
One theory about the origins of the rhyme is that it is descended from Old English or Welsh counting, similar to the old Shepherd's count "Yan Tan Tethera" or the Cornish "Eena, mea, mona, mite".
Another possibility is that British colonials returning from the Sub-Continent introduced a doggerel version of an Indian children's rhyme used in the game of carom billiards:
ubi eni mana bou,
baji neki baji thou,
elim tilim latim gou.
...
Another possible origin is from a Swahili poem brought to the Americas by enslaved Africans:
Iino ya mmiini maiini mo.
Most likely the origin is a centuries-old, possibly Old Saxon diviner rhyme, as was shown in 1957 by the Dutch philologist dr. Jan Naarding, supported by prof. dr. Klaas Heeroma at the Nedersaksisch Instituut (Low Saxon Institute) at the University of Groningen. They published their findings in an article called
Een oud wichellied en zijn verwanten (An old diviner rhyme and its relatives). In part I of the article Naarding explains, why the counting rhyme he found in
Twents-Achterhoeks woordenboek (1948), a dictionary by G.H. Wanink, stands close to an early mediaeval or even older archetype. That same version was recorded in 1904 in Goor in Twente by Nynke van Hichtum:
Anne manne miene mukke,
Ikke tikke takke tukke,
Eere vrouwe grieze knech,
Ikke wikke wakke weg.
Naarding calls its origin 'a heathen priest song, that begs the highest goddess for an oracle while divining, an oracle that may decide about life and death of a human'. The first lines can be translated as 'foremother of mankind, give me a sign, I take the cut off pieces of a branch (= the rune wands)." This explanation was revived and extended in 2016 by Goaitsen van der Vliet, founder of the Twentse Taalbank (Twents Language Bank). The last line of the rhyme (in the Netherlands degenerated to 'iet wiet waait weg') can be translated as 'I weigh it up' (in Dutch 'ik wik en weeg').