This page offers a guide on how to enter Gerudo Town during the Forbidden City Entry quest.
Main Quest: Forbidden City Entry
Obviously we need to get into Gerudo City so that we can board the Divine Beast Vah Naboris, but unfortunately nobody knows that we are a Champion so it’s time to fake it.
Head back to the Kara Kara Bazaar and go into the tall, clay building. Speak to the Gerudo there and they will mention a strange Hylian who hangs around on the rooftop of their building during the day. If it’s not daytime, sit by the nearby fire to pass time until noon.
Climb the ladders up to the rooftop and speak to the man in pink, Vilia. As you progress through the conversation, opt to say, “You’re very beautiful.” Flattered, Vilia will offer to sell you a set of your very own woman’s clothing. You will have to buy it, so cough up the 600 Rupees (and sell stuff if you don’t have that much) and put it on.
This armor set is actually heat resistant so even though it looks tacky (well, we think he looks quite charming) it is useful. Return to Gerudo City either by taking the foot path or fast traveling to the Daqo Chisay Shrine and now you can freely enter the city without the guards stopping you. Once you have entered Gerudo City, the main quest will be complete.