Neutral is supposed to introduce less foreign tint into objects' own colors, hence "neutral".
This is distinct from high CRI, which focuses on color reproduction specifically, but the way CRI is calculated currently may allow for a very significant reddish/yellowish tint (90+ CRI XM-Ls are 2600–3200 K, which is why they aren't very popular even with custom manufacturers).
A highly neutral (say, 4500–5000 K) low-ish CRI light could make all colors look equally bleak, for instance, while a high CRI non-neutral light makes them look vivid but may introduce chromatic distortions of its own.