V1.16.4-1.6.0 in FTB Academy 1.16:
Any furnace marked with the tag 'betterendforge:furnaces' cannot be accessed.
Blast furnaces and smokers are unaffected, but the regular furnace and it's variants (endstone/etc) don't show the GUI when right-clicked. The player's hand swings to no effect like they were clicking a sign.

I have to assume this is some conflict with 'fastfurnace' as I see nothing else in that pack that directly affects furnaces, but I don't know enough about modding to say why.

Cannot reproduce, closing for now.