I avoid eating "Blood" whether directly or indirectly, as via Meat from an Animal that hasn't been properly slaughtered ...
Please correct me if I'm mistaken, but isn't that a commandment that the Gospels retained?
If you look up the parallell in the Hebrew Bible (Leviticus 19:26, also Samuel I, 14:33), you'll see that this isn't only a dietary law, but a prohibition related to an idolatrous practice (Nachmanides commentary on Leviticus). It would make sense that early Christianity retained this, even after rejecting Torah ritual and dietary laws.
I know that J's Witnessess take this as a prohibition of accepting transfusions - something completely divorced from the sense of the Biblical text.