If there is an item in the output slot the furnace stops cooking food, ores, or anything like that.

Only works if FF is installed alone.
It's a conflict with CustomNPCs

The issue is in The SM Modpack + and other modpacks that have fast furnace and CustomNPCs installed

You can Download the SM Modpack to see it

it's a bug in custom npc's

But how can it be fixed?

I am interested in fixing this issue.

Just tell me how you found out it was CustomNPCs and i will try to fix it.

Ask Shadows-of-Fire he said it was bug with CustomNPCs