Correction, Tolkien uses 'man' for 'human' in general, following Old English semantics.

More accurately it'd be, "are you were or wife?"

Thus it came to the ears of Hobbiton that a guest was come, who asked of Pippin whether, as one of the Men, he was a were or wife. "Neither", Pippin declared: "I am an Hobbit". But the visitor was yet unwilling to yield, and asked once more which was the matter below his belt. "Food, I suppose, my sir; elevensies, lunch, and possibly an afternoon meal, if I will."

"What's in Frodo's trousers?"

Golum and Samwise in unison: "My precious" 🥵

"What's in your trousers?"
Bilbo: "Guess!"

They are a different race, what if they have different genitals? Or no genitals? They might not even reproduce what if they just grow from mushrooms in the woods and there entire purpose is to die on the mushrooms and bring all that fertilizer back to the fungus?

Hobbits and hobbettes.

Dwarfs and dmarfs.

"It's true, you don't see many dwarf women. And in fact they're so alike in voice and appearance, they're often mistaken for dwarf men!"

(Whispering) "It's the beards."

I was never quite sure whether Aragorn meant "beards are how you tell them apart" or "the women having beards are why they're so often mistaken"

How do they figure out which bathrooms to use without major incidents!?