Good question. I'm an author on both of the new CD47 studies, so I'll try to answer this for you:
1. CD47 appears to be higher on tumor cells than on normal cells. In general, the higher the expression of a marker on a diseased cell versus a healthy cell, the more of a therapeutic window/index [1] that is available for a treatment to specifically target diseased cells.
2. Inhibiting the anti-phagocytosis (i.e., "don't eat me") signal is only half of the equation. There are also pro-phagocytosis (i.e., "eat me") signal(s) that also are present [2] and that play a role in whether, and how well, macrophages, and other phagocytes, can phagocytose a cell. "Eat me" signal(s) also differ between normal and cancer cells, adding more nuance to the situation.
It does sound like a very promising avenue, but I imagine that this route could still be a problem for people already pre-disposed to autoimmune diseases. Still, most of those aren't as bad as the alternative here. Any drug based on this doesn't have to not have side effects, it just has to be better than normal chemotherapy.
You raise another good point here, that the allowable side effect profiles for cancer drugs are much less stringent than for drugs indicated for less life-threatening diseases.
I think the key is that Cancerous cells expressed a higher level of this marker leading the Immune cells to destroy them specifically.
However there is also this line "Although macrophages also attacked blood cells expressing CD47 when mice were given the antibody, the researchers found that the decrease in blood cells was short-lived; the animals turned up production of new blood cells to replace those they lost from the treatment," so this seems like a very valid concern.