https://streamable.com/vllgai
Here's the video to show that the mod isn't really doing what it meant to do

The fire overlay is completely gone, even without fire resistance or in creative mode
I first thought it was just the "Short Fire overlay" texture from Vanilla Tweaks broke it so I removed the pack, same issue

This mod doesn't remove the fire texture on burning entities, only the fire overlay that you see in first person. No idea what's going on in that video. Are you sure Why Am I on Fire is causing that? What happens when you remove the mod?

nothing happened, the fire overlay is just gone
At first I thought my fire texture is transparent (which will make them invisible, I assume) so I go back to Optifine to test, and the fire overlay is still there,
Going back again to Fabric, before I have the mod, the fire overlay works fine, after I install it, the fire overlay is just invisible in my perspective, removing it doesn't fix the problem

This mod doesn't remove the fire texture on burning entities, only the fire overlay that you see in first person.
No idea what's going on in that video. Are you sure Why Am I on Fire is causing that? What happens when you remove the mod?