When using the Enhanced Block Entities mod, with enhanced chests enabled, chest, trapped chest, and ender chest models are invisible.

Effective doesn't touch the rendering of chests at all, only hooks into the opening animation for bubble spawning underwater, what makes you think this is Effective's fault?

I tried it alone with just effective and the enhanced block entities and it works fines, I also tried a few other big performance and helpful mods and it still works.
Chests looked fine to me I think it's just a video problem