The great philosopher, Ted

So if someone loses their p**is in an accident, etc, they aren't any gender at all?

They are genetically male. Looking for a vag or peen is a shortcut to doing a genetic test.

Nothing intrusive about that

And what about people born with ambiguous genitalia?

Genetic test.

If you get both arms cut off in an accident are you suddenly a worm?

I'm not the one making the argument that identity is determined by which body parts someone has or doesn't have

"So if someone loses their p**is in an accident, etc, they aren't any gender at all?"

You asked the question

No you a man with no arms.
If you cut off your p**is your a man without a prnis, not a woman