I pick up my prescriptions in person at a local drugstore. The first few times, I was presenting male. Since then, I have presented as female. I have had no problems.
Pharmacists are trained to be discrete, and as others have pointed out, there are legal protections in many places requiring them to be discrete. When I started out, I had my doctor list my name on the prescription as "<deadname> (Kathleen) <lastname>". It was fairly obvious what the prescription was for. The only awkward question was which name I wanted them to use. Now, my prescriptions are written out just for Kathleen.
They do ask if you have taken the meds before. That is a requirement, because they have to ensure that you know how to take them.
I resolved when I transitioned that I would have no more secrets. So, if a pharmacist had asked me the purpose of the prescription back when I was presenting male, I would have told them: gender transition. I am not ashamed of who I am. Knowing the purpose helps them to be confident that I am getting the right meds. Nowadays, I don't worry about it at all. I am just a [possibly trans, possibly post-menopausal] woman picking up her HRT meds. Happens all the time. Nothing to see here, folks.