To be neutral and do nothing, is indeed siding with the oppressor.
As for your analogy: You are describing legal and acceptable competition between diners, which is not comparable to the situation here, unless diner A initiated an unjustified, violent, irredentist war of genocidal conquest against diner B, for which diner A has been condemned by most countries in the world, and also diner A's leader is wanted for war crimes against children committed while prosecuting this war, and is evading arrest.
If that is the case, then yes, remaining neutral or choosing diner A, is indeed choosing the side of the oppressor, and such a choice would reasonably reflect poorly on you.
This formulation states that since every act will inevitably in some way favor one party, every single act is moral, which to me seems fanatical, absolutist, and frankly unlivable.
That's fine, and neutral in the quote by Desmond Tutu refers to both intention (being in favor of injustice) and effects (effectively supporting injustice, even if that is not your primary intent).
> Otherwise the word "neutral" no longer has any meaning
That's a bit self-centered, innit? 'If you don't agree with my personal definition of this term, the term has no meaning.'
> Indifference is not evil
Indifference/neutrality in situations of injustice can absolutely support the oppressor, which is the entire point of the quote. Indeed, someone with no empathy for those affected by their actions would be meeting at least 1 criterion of sociopathy.
> This formulation states that since every act will inevitably in some way favor one party, every single act is moral
You seem to be skipping over the "in situations of injustice" part of the quote. Most countries agree that russia's violent, irredentist war of genocidal conquest is an injustice perpetrated on Ukraine. The same cannot be said about 2 diners competing.
