See below for an explanation of what "incompatibility" means in AoW3.

Compatibility mods which exist for the PBEM & SP balance mod
- Empire Building Mod: https://steamcommunity.com/sharedfiles/filedetails/?id=947634602
- Weapon Resize: https://steamcommunity.com/sharedfiles/filedetails/?id=1555900865
- The League of Extraordinary Builder: https://steamcommunity.com/sharedfiles/filedetails/?id=1542043724

Mods which should not have inconsistencies with the PBEM & SP balance mod, i.e. "compatible"
In general: all mods that add new content but do not modify stuff in the base game, and especially stuff modified by the balance mod. That means most of the mods are "compatible" even if only a few are actually listed below:
- Chivalrous Intentions - however, Thunder Braves and Breechloaders's Fire Musket is not modified as Musketeers in the balance mod for instance
- Less T4 Unit Spam (For AI)
- Old Man and the Sea
- Racial Heritage

Mods expected to have inconsistencies with the PBEM & SP balance mod
Please note that you can still use those mods with the balance mod but there will be some inconsistencies.
- Structure Reward Variety - Spring of Life changes from that mod might be ignored or replace the change in the Nymph reward from the balance mod. The Strong Defenders Normal Rewards mod should prevent all the changes from that mod (i.e. totally "incompatible").
- Hero Development mod - heroes & Leaders might get abilities they shouldn't (likely that Hero Development modifies some hero upgrades also modified by the balance mod) but this should be rare (no such problem reported so far).
- Extended Settings - Huge and Gigantic map sizes not available and replaced by Small Square and Medium Square (fixed in v1.3)

Mods which do not work with the PBEM & SP balance mod
- Chinese language pack - all mods which change vanilla game's descriptions will be overwritten by the balance mod (if they have a priority 0), since it also updates all the description in order to provide an improved French localization. Since this "language pack" mod rewrites all the English description into Chinese, it is 100% made dysfunctional by the balance mod.

What incompatibility means
If mod "A" changes, say, Mark of the Heretic and increases its cost to 50 CP, and mod "B" doesn't change Mark of the Heretic, then both mods are compatible. But if mod "B" changes Mark of the Heretic too to decrease cost to 10 CP, then they are "incompatible" (but that word is not really appropriate as it's confusing and let people think it will cause troubles) in the sense that the contradictory changes can't be applied simultaneously. What the game will do is that it will pick the change from the mod with the highest priority, or from one of them if they have the same priority level. So in the end, you'll end up with 10 or 50 CP depending on priority. But you won't get any error or any issue.