When I emerged, I joked to a Target 20 something employee who was hawking their credit card behind a podium that I should have declared myself a woman and gone to the other one. She said that while corporate might have condoned it, she would've enforced local standards and had me arrested if I tried, LOL!
You don’t just get to go into the women’s washroom at Target, the full policy in such matters is you can enter the dressing room or women’s locker rooms or even showers (at gyms).