I highly doubt that. We saw that clothes shop in the Town on the second island, surely they wouldn't close that off until post-game. I would see absolutely no benefit of doing that, especially since they made a point of character customisation in the latest trailer.
Yeah, I thought that "postgame only customization" claim would be fake. The question is, will there be a clothes shop/salon on every island? Because I'd imagine those who don't like the default protagonist designs will want to know how soon you can start getting the clothes and hairstyles.
Like X/Y, I could see each clothing shop have different clothes that change every day.