In linguistics there is a term horror aequi, referring to a tendency to word sentences so as to avoid repeating the same grammatical structure consecutively or nearly consecutively.
This term was coined fairly recently, in 1909, and the study usually cited to explain it is "Cognitive complexity and horror aequi as factors determining the use of interrogative clause linkers in English" by Günter Rohdenberg, in Determinants of Grammatical Variation in English (2003), p. 205. An example from that article:
(1) She was at a loss to know what to do.
(2) She was at a loss to know what could be done.
The horror aequi principle says that speakers will tend to favor (2) because it avoids the unseemly repetition of to <verb> in (1).
It sounds like horror aequi was coined in imitation of horror vacui, but I haven't tracked down the original article yet to be sure.
Both vacui and aequi are genitive forms of an adjective. I understand horror vacui to mean most literally "dread of empty space". That is, the adjective is used substantively (as a noun), so it means "something empty". Horror aequi thus means "dread of things that are equal".
Someone with a better feeling for Latin will have to confirm this (maybe in a comment), but it sounds like Joonas's answer might fit your meaning more precisely even though it doesn't parallel horror vacui as closely, because you mean not a dread of things that are equal, but of the abstraction of equality—aequalitas rather than aequa.
By the way, when writing that last sentence, I chose "precisely" to avoid repeating "closely".