Can you point me to which verse you are referring to? The points that DanielH mentioned from Acts seem to clearly set aside consumption of blood as a different matter from the full dietary laws of the Mosaic Law.
Ok, so Acts 15 is about the followers of Christ turning away from the Jewish laws such as circumcision and unclean foods/acts etc.
This was because, up to this point, the followers of Christ were Jewish and continued with the Jewish rules they grew up with.
However, there were now a lot of non-Jews turning to Christ and Paul and others realised that they could not force Jewish rules on non-Jews when Christ explicitly said those rules meant nothing, the only way to salvation was through him.
They decided that some things should still be outlawed and those were things that were linked to animal sacrifice, including the consumption of blood.
Jesus has himself stated that the consumption of any food would not be a bar to salvation in, for example, Mark ch7 v19.
It would appear that the ban on eating blood was something that was to appease the Jews as they found the practices of the non-Jews in regard to food as particularly disagreable.
Later, in Romans chapter 14 Paul tells us not to judge people on what they eat.
So, in conclusion the original rule against eating blood, particularly from a strangled (ritually killed) animal was due to its links to pagan sacrifice rituals, and how it annoyed the Jewish followers of Christ.
Later on it was seen as a cultural thing, to be avoided around touchy Jews.
Then it was seen as something that should not be worried about, let alone enforced.
As any blood you eat now would have nothing to do with a pagan ritual, then you should consider it ok to eat, especially if it is your peoples heritage/culture to eat that food.