This issue does not occur on single player worlds. Only on multiplayer servers. The log linked below represents an absolute minimum of mods installed, a fresh world, and stock configs for both mods. Server starts fine for each mod when the other is excluded. Other details:
Forge 1.7.10_1208
Java 1.7_67,
OS is Linux Mint 17 x64.

Full Log on Pastebin: http://pastebin.com/p25Y0Yi9

I will also post this issue to AM2's tracker for convenient collaboration.

Is there a way blacklist mods so JAS ignores them? Then the blacklisted mobs just won't spawn, or spawn with the mod's own internal spawner (if it exists).

This error in the past has indicated a mod is registering an entity on the server-side that cannot exist there (has client references), so when JAS analyzes (not spawning them, just checking information about entities in the list) the server-side entity list it causes a crash.

JAS currently does not have a work around for mods that do this.