Of course the FDA is not, itself, a democratic instution. But then neither is your local police department or NASA. The reason those institutions are accepted despite the lack of direct democratic accountability is because they are still situated within the larger democratic institution (the US government) and subject to oversight by those elected representatives.

If you hate the FDA your best bet is to lobby against it yourself (or help others that do). Its to much of an in-the-weeds issue for it to be a high priority for most lawmakers (unless maybe you live in a district with a lot of businesses regulated by FDA)