Donated blood is stored as packed red blood cells, with the plasma removed. The plasma is where most of the hormones reside while being transported, so in packed RBC transfusions, there will almost no transfer of hormones. This makes it so that blood type is pretty much the only important factor when determining whether somebody can receive blood.

Sometimes doctors do perform whole blood transfusion which does not have the blood plasma removed. This has the chance of increasing hormonal levels temporarily in the recipient. However, the body will quickly compensate and bring levels back to normal. Even if not, the hormones will still degrade and lose their effectiveness over time.

Side note: everybody has both male and female hormones in their body, at different levels. These levels can change a lot depending on your age, genetics, menstrual cycle, or even the time of day. As long as there is no prolonged increase in the levels of a particular hormone, there won't be any abnormal effects.