I can't really follow how a woman showing an ID to a lecherous cashier allows said cashier to stalk her online. Where she is, presumably, speaking about personal experiences anonymously.

Generally you can't get through life with no one knowing your name; even women at risk of stalking. As you already pointed out they may have to show ID to police, university staff, employers, landlords, medical staff, banks, social workers or other government employees. Buying a single-use token annually to get on social media doesn't meaningfully increase that risk profile. And as I already said, if they're that worried, they can ask a friend to buy it for them.