A Proof For Humanism(?)

This randomly occurred to me the other day, not sure of its import. Starting with an easy one:
P1

1. Anyone who identifies as a woman is a woman.
2. Not everyone who identifies as a woman feels safe doing so publicly.
3. From 1 and 2: Someone who publicly identifies as a woman could truly identify as a man.

I also think the following is uncontentious:

P2

1. Anyone who identifies as a man is a man.
2. Not everyone who identifies as a man feels safe doing so publicly.
3. From 1 and 2: Someone who publicly identifies as a man could truly identify as a woman.

This generalization might be a little shaky, but let's run with it anyway:

P3

1. Anyone who identifies as <Gender X> is <Gender X>.
2. Not everyone who identifies as <Gender X> feels safe doing so publicly.
3. From 1 and 2: Someone who publicly identifies as <Gender X> could truly identify as any gender.

From P1 and P2: 

• Someone who self-identifies as a woman could be a man or a woman.
• AND
• Someone who self-identifies as a man could be a man or a woman.
• THEREFORE
• You can't tell whether someone is a man or a woman, regardless of how they self-identify.

If you accept P3 as a valid generalization, this becomes

• You can't tell what gender someone is, regardless of how they self-identify.

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Assuming you buy the line of reasoning above, you're left with something of a dilemma: How do you treat people if you can never truly know their gender? The solution which occurs to me is that you treat each person in a gender-blind fashion, as a person with their own intrinsic dignity. Which sounds a lot like the "humanism" side of the old "feminism vs. humanism" debate.