Basically, for some reason, the Move Item for fast crafting does not recognize logs, any type of log, not from Vanilla, or mods.

Thanks for the report!
That's very strange, but I wasn't able to reproduce this issue with just JEI and vanilla.
Can you try to remove some mods and see if one is causing the issue?

This was fixed in the latest update, where logs and planks are now picked, regardless of the type.

This issue is now showing on the glass block. Where if I have a recipe that uses any glass block, but the current repipe is showing a glass block form a mod, no glass block that matches that specific type will be used.

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