No we're not talking about the present. We're talking, at latest, of the contents of The Gathering Storm, as I corrected two posts ago. As for the Black Tower, I've already addressed this. The entire operation was handled in secret. Pevara recounts in Remember the Old Saying how she had to search for tiny clues to find Red Sisters to involve in the operation. This is not 'the Red Ajah' having greater priorities, it is Tsutama Rath having greater priorities. And good for her. I don't expect every Aes Sedai in the Tower to be an idiot.
So, F-T, you admit that the Highest of the Red Ajah thinks there are more important things than the Rebellion and supporting Elaida. The same is the case with a highly influential Red Sitter, Pevara. It is also true of the former Keeper of the Chronicles, Tarna. Another Sitter, Javindhra, who may not agree with such policies, has been quelled by Tsutama into following her idea, and is now in the Black Tower.

We also know from Egwene that it is likely that Tsutama has spoken to Elaida and asked her to lie low, that the Reds cannot afford to support her if she blunders much more.

With almost all the high command of the Reds either more concerned about the BT and the DR, or else under orders from Tsutama to make themselves so, exactly why is it a stretch to believe that she ordered them to shut up about the Logain issue, accept the fact that the new Amyrlin seems reasonable and had raised one of their own as Keeper, and let bygones be bygones? Seems exactly what Tsutama would order, and given the sort of power the Highest wields, I don't see why this is improbable.