Probably, most people will be happy with emitters spot on black body line (duv +0.001 to –0.001). I think, reddishness (or rather rosiness) to duv –0.003 is acceptable (and helpful with recognizing blue and red details), below that I consider it a bit of special use.
In practice, while SST-20 LEDs are promised to be on black body line with tints FA2, FA3, FD2, FD3, they are a bit more yellowish, when used on lower currents. This is why SKV89 recommended to source the tints above (FA1, FA4…), because they can hit the black body line better (especially, when not just bare led is measured, but optics as well).
In practice, I found the FB4 tint of SST-20 very appealing for outside use, if it is driven around 2A, because the tint changes, so it is noticeably rosier, than if multiple same LEDs were driven at a much lower current each.
It is very difficult to source Nichia 219C with proper duv values, and this is more visible for emitters in the 2700K-4000K CCT range. But for me, even a slightly greenish (duv up to +0.003) 219C is fine, if they are in the 5000K-5700K CCT range.
To cover the ‘cool white’ range of CCTs with high CRI emitters, do you consider to get Samsung LH351D emitters (they have 90 CRI for both 5000K and 6000K CCT)?
Those emitters are a bit less throwy, than 219C, but overall, they have somewhat more output (also, it is safe to drive them far past 4A with good heatsinking) - and maybe a bit less green.