A double blind study means neither the patient nor the doctor knows whether they're in the treatment group or the control group. It has nothing to do with what is used as the control. When there's an existing safe, effective vaccine, you always use that for the control group. It would be unethical not to. It's still a double blind study, because the patient still doesn't know whether they're getting the new vaccine or the old one. And it makes the resulting data stronger, not weaker. It tells you whether the new vaccine is more effective than the old vaccine, not just whether it's more effective than no vaccine at all.
When there's no existing vaccine, then you use an unrelated vaccine as the control. That's essential. If you used an inactive placebo as the control, and a patient felt tired and achy the day after getting the shot, they could be pretty sure they were in the treatment group. That knowledge could affect their behavior and bias the results. So instead you use an unrelated vaccine with similar side effects as the control, so the patient can't infer which group they're in from side effects. This is standard practice.
But RFK has arbitrarily declared that won't be accepted. Instead you must use an inactive placebo, even though that gives worse quality data.