There are lots of conflicts between these two mods since they both edit lots of the quests that govern the race specific and other Dialogue, like in http://bildr.no/view/730576.
From what I've gathered both mods don't want their NPCs from their new factions to use generic dialogue so it's mostly cosmetic and nothing game breaking if one mod's changes is overruler by the other one.

Is it possible to merge the Conditions into a patch, or to give the vanilla Quests that the mods edit new Form IDs (and then update the relevant references) to avoid conflicts? I now the latter is an easy solution when mods edit vanilla records like Containers, but Quests and associated Dialogue is much more complicated...

Uh...BTW, the "Important" in the subject should read "Important or not?".

Possible, yes, but it has to be something you tailor to your own collection. Trying to turn it into a filter patch won't work. And when I tried to force the issue just now (by deleting one of the mods) to rebuild my own cobbling of this sort of thing, Bash spectacularly failed to notice it forced the Bashed Patch to be marked as active despite it having a missing master.