Well it wasn't part of the original problem statement, so the solution allows sort to pick any order it chooses for elements with the same vowel string. You can tack on the original word to the end of the vowels string to sort by consonants when vowel strings match.

Here is that idea, but using GRT Sort instead of ST:

use 5.014;
say join ', ',
    map {s/.*\0//r}
    sort
    map {tr/aeiou//cdr."\0$_"}
    qw( xexix babebib xaxexi babebibb );
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babebib, babebibb, xaxexi, xexix
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