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According to Wikipedia, two different word forms (allomorphs) can actually be different "faces" of one and the same word (morpheme). An example is the English indefinite articles a and an.
Since redact, react and re-act are pairwise different in terms of meaning, are there three different morphemes derived from Latin re-?
It depends entirely on your theories of morphology, syntax, semantics and phonology. You inject the possibility of the words being different in terms of meaning as relevant, so we can start semantic differences. Obviously react and re-act are different in meaning, but so are re-surface and re-consider. In that case, is the difference because of re- or is it because of the root? Or is it because of an interaction between the prefix and the root? Typically, one looks for a common semantic property that unifies all instances of a morpheme, therefore we are allowed to disregard some meaning differences between two words, such as the general meaning "act again". Under a strong compositionality requirement for morpheme status, it would be required that every morpheme must have a constant semantic value that holds of all of its occurrences. Under that view, "kick" is not just one morpheme, it is many. As far as I know, nobody adheres to such a strong compositionality requirement in morphology.
From the syntactic perspective, "being a morpheme" is generally held to be "being an element that can be combined with other elements according to some rule". We do not treat re in region as a morpheme just because it contains re, we would look for evidence that re occurs with other things, and that the other things are also morphemes – but we don't say that gion is a morpheme just because you can parse it out of the word region. The other syntactic requirement for making a claim as to morpheme status is that there is some syntactic or semantic function associated with the putative parts. There is no syntactic or semantic function associated with the parts of redact, for example you cannot subdact, prodact, addact, transdact and you certainly cannot dact a thing. The word redact is like region (synchronically), it is a root not composed of parts.
There is weak evidence of combinability in react, see interact, counteract, exact, transact. There is also a shred of evidence from phonology that certain polysyllabic words are analyzed as prefix plus root, namely the stress pattern of perˈmit and company, where the expected location of stress in a verb ending in a short vowel and single consonant is on the penult. However, the phonological consideration does not support a bimorphemic analysis of react since the root ends in a consonant cluster which would attract stress anyhow.
In other words, whether or not all instances of re in English reflect a single morpheme, or different morphemes, depends on the criteria for morpheme status that you assume. We could accept re in redact as a prefix if we also include "comes from the same historical root", in which case there would also be a shared morpheme in mother, maternal, feather, archaeopteryx or acre, agriculture.
The term "allomorph" is used in linguistics in many different ways. The uses do all assume some concept of "a (single) morpheme", and "allomorph" has to do with "different realizations". That difference might be in terms of a phonetic property, but generally the term lumps together "phonological adjustment to the phonological substance of a common underlying form" such as the alternations in the plural -s or the past -ed, or else "selecting a specific phonological underlying form of a morphosyntactic feature matrix", such as the fact that subject agreement in Arabic verbs is completely different between perfective vs. imperfective inflections. Since re is not a single prefix (in most accounts) given your three examples, this would not be "allomorphy".
