Peter, I'm wondering if you raised the question a second time to track whether views have shifted? Maybe you tried buying women's clothes in the past, or wanted to try, and found it wasn't well accepted where you live, or feared it might not be.
And that was going to be my reply -- it very much depends on where you live. I say this because I'm a crisis counselor and when the users of our service have a crisis that involves gender-nonconforming behaviors, they are pretty much never from major liberal cities such as New York.
Also, internet shopping means that pretty much anyone can buy pretty much anything in total privacy, even if you live in a place that's less open-minded than NYC, but if it's the actual shopping experience you're after rather than just owning the clothes, I'm with minimalist -- find yourself a worthy wing woman and forge ahead.