I like your emphasis on action, rather than identity, here. Yet whether it is used as a verb or a noun, the label of "ally" may be doing more harm than good.
An “ally” may not be an enemy, but they are still the “other.” Therein lies the problem. It is, by definition, a temporary relationship. It usually requires benefits to both sides to maintain. Thus, as you note, white “allies” whose guilt is not sufficiently assuaged will tend to abandon the relationship.
It is this sense of “otherness” which underlies racism itself — the fear of the threat of the “other” and the myth that I can only advance if I set you back. Rather than creating a competition between individuals I argue that we must think in terms of how to raise the welfare of all.
The true opposite of racism is not anti-racism, but solidarity. “Solidarity,” as I like to quote Ricardo Flores Magon (the anarchist from Oaxaca who started the Mexican Revolution), is “the consciousness of the common interest, and the actions which follow from that consciousness.”
Allies come and go. Solidarity is Forever.