This is not a silly question. While transfusing white blood cells, with the CCR5 mutation isn't a solution because these cells will be rejected by the recipient's body (and also because those cells have a limited life time), transplantation of so called "stem cells" have provided promising results in HIV+ patients with blood cancer undergoing stem cell transplantation.
So to summarise (the protocol is quite complicated but since you mentioned you are not in the biomedical field, I will try to explain it in a simple way), these patients receive an ablative chemotherapy (+/- total body irradiation) in order to destroy all their "cancerous" cells. They then get transplanted with stem cells from a donor which has the CCR5-delta32 mutation. These cells then replace the previous population of white blood cells (which have been killed during the ablative phase) leading transplanted individuals to become HIV resistant.
So, now, you must wonder while this has not been more used?
- Because this method is very toxic and associated with several complications (ex: patients undergoing this high risk ablative therapy are at risk of developing infections during the process as their immune cells get destroyed)
- Patients need to take immunsuppresive therapy for a long time to avoid rejection of the transplanted stem cells and theses drugs are also associated with side effects
- Studies have still to show whether this method is at least as effective (in terms of short and long term outcomes) as taking HIV drugs (which become more and more efficient) in healthy individuals (remember that this method was used in HIV+ patients with blood cells cancer, who, anyway, needed a chemotherapy)
Hope this provides some clarification to your question!
Here two references (which provide a good understanding for the layperson)