Do Red blood cells(mammals) really have no organelles?
Yes. This is true. During the final stages of red blood cell formation in the bone marrow, the nucleus and several other organelles are broken down and/or expelled from the cells. In the process they decrease markedly in size, from about 24 to about 7-9 micrometer. Presumably this makes them small enough to pass through the smallest capillaries. Lacking those organelles also limits their life expectancy to approximately 120 days.