Italian 2.54x24 and BSC 1"x24 are very similar, with the same pitch and outside diameter. However, it's a case of close but no cigar.

BSC threads typical modern threads with a 60° profile and flat tops and bottoms. Italian threads are Whitworth with a 55° profile and rounded tops and bottoms.

There are also slight difference in the pitch diameter which determines how the parts actually fit together. There are also tolerance issues and your fork may be at the high end of the range and new headset at the low end.

Before doing anything, I'd borrow another BSC headset and see if that fits OK, If so, exchange the new headset. If not, running a die down your fork will shave some material where it counts and allow a BSC headset to fit correctly.