If two people ate the exact same thing, would their farts smell the same?

I think the smell would be similar but not exactly the same.

Nah. Every fart is different. Like our own personal aromatic signature. Sort of a fartprint if you like :¬)

Each person’s own chemistry and internal fauna would play a part. The smell would be unique.

Just like I always said “My farts don’t smell”.

@Tropical_Willie

That’s right. YOU smell, your farts STINK.

my wife and I fart the same

It is possible but they would have to have the same bacterial makeup for digestion.
That could be accomplished with the same diet as @woodcutter.

No. I distinctly remember reading somewhere, probably national geographic many years ago, that people from the same tribe in Africa could tell who a pile of dung belonged to when they came upon it on a hunting trail, because each member of the tribe’s dung smelled differently even though they had similar diets. Maybe thats too much info, but seems salient and valid.