When I first bought women's clothing, it was a little bit nerve-wracking for me at first as well, since those of us assigned male at birth typically grow up viewing that behavior as taboo. It can take a little bit of desensitization for us to get over this culturally ingrained closed-mindedness.
The first time I bought women's clothes a few years back, I bought them from a store that sold both men's and women's clothes (it was a Forever 21 store with a fitting room area that was used by all customers regardless of gender). I quickly learned that no one cared about what I was trying on and purchasing (fast fashion stores like F21 and H&M are very "hands-off" in terms of associate involvement with customers). Once I had several feminine outfits in my wardrobe, and could therefore start appearing feminine in public, I built up the courage to start shopping in women's only stores along with department stores.
I have since moved beyond fast fashion for my feminine outfits, and have started shopping at more upscale stores in a desire to purchase higher-quality, versatile items that will last for many years to come. These days my favorite stores for women's clothing are probably Nordstrom and White House Black Market. One of my favorite items I have since purchased was a
reversible dress from WHBM (online link included for illustration purposes only). The patterned side of the dress seems less forgiving on my body type, although it also functions as an LBD with the solid black side facing outwards.
And I've actually come to enjoy shopping at stores with high levels of customer service. I've only been misgendered once (at a women's only store, to my embarrassment... I was more worried about the other customers' reactions than that of the sales associates, although I did kindly correct the SA on my preferred pronouns as it was probably just a slip of the tongue) but it didn't impact the customer service I received or the willingness of the sales associates to serve me. Come to think of it, in the end sales associates just want to make a sale (and possible commission money), so it doesn't make much business sense to discriminate against a transgender customer.
Also, if you're worried about trying on clothes in the store (and don't think you "pass"), at pretty much every women's store I've been to, I've always seen guys waiting around for their significant others and/or female friend(s) in the dressing room area when their SO or friend tries on clothes. If you think your gender assigned at birth is an issue, imagine for a moment that the aforementioned guy were actually interested in the women's clothes at that specific store for some reason. Logically it's not that much more of a step to go from waiting on somebody else trying on clothes to you actually trying on clothes yourself from that point.
Most of the worry about us shopping for women's clothes, at least based on my experience, is pretty much all in our heads.