I would argue it does make a difference. Like I said, many people don't fit gender norms, but most people do. So knowing it's a woman shopping can suggest a array of things.

She will likely be buying some degree more female-oriented or marketed products, a strong example being tampons or a weaker example being beauty products
Her experience shopping will be that of a woman's, i.e. she might get patronised in the hardware section or sales-bullied in the technology section, both of which are quite common for women even now

I really can't think of an example where you interact with other people where a woman's experience won't be affected by her being a woman.