This bug report may should instead fall onto the shader, but here's what I got my bug boiled down to:
Shader + an enchanting table resource (includes optifine-styled emissive textures) + continuity with emissive textures on

Minecraft 1.21.1

Fabric 0.16.10
Continuity 3.0.0+1.21 or 3.0.0-beta.5+1.21
Complementary Shaders - Reimagined r5.2.2

• RP Support: Integrated PBR+
• Performance Settings > Shadow Sample Quality: Off or Very Low
  Fabric API 0.115.0+1.21.1
  Iris Shaders 1.8.1+1.21.1-fabric
  Sodium mc1.21.1-0.6.5-fabric

Better Enchanting Table 1.2 by Jacosvaldo

The last piece to this enigma is that the mob emissions are dependent on what item is right-most in your hotbar. I did not test non-hotbar inventory positions. Sometimes, angle of sight / edge of your screen, or where you are rotated around mob also influences the effect.

Bug is removed by turning off emissive textures in continuity settings, changing one of the two shader settings mentioned, or unequipping the resource pack. I did not check with other emissive resource packs.

Screenshots below show an affected mob. The item does not need to be held for this effect to activate, it just needs to be right-most in hotbar. Held to show what item was causing what effect (it's curious!). Additionally, effect is removed if F1 is pressed to hide GUI.

Continuity does not interact with or directly affect the rendering of entities. Report this to Iris; I cannot do anything about it.

Thanks for the clarity on where to go! I confirmed this doesn't happen with a different mod that does block entity emissions, and it seems there's another issue with shaders + emissions, too. So hopefully Iris can do help me pin it down! Thanks a bunch and thanks for having an awesome mod that's a great staple everywhere :)