The supposed inconsistency here is clearly that some passages say it's OK to eat anything, but that in Acts 2:15, James judges that non-Jewish Christians should be "not troubled" with the Law except as follows:
19 “Therefore it is my judgment that we do not trouble those who are
turning to God from among the Gentiles, 20 but that we write to them
that they abstain from things contaminated by idols and from
fornication and from what is strangled and from blood. 21 “For Moses
from ancient generations has in every city those who preach him, since
he is read in the synagogues every Sabbath.”
So, in some passages, they say it's OK to eat these things, but in Acts, James says it's not.
The difference in context is, again, obvious. All of the other passages are clear that eating a particular animal is not a sin. Meat is meat. So the question that must be answered is, why the restrictions in Acts 15?
There are several, but the most consistent with overall Scripture is that it's given so that the Gentiles won't be stumbling blocks for the Jewish Christians, as described in 1 Corinthians 8 (NASV):
1 Now concerning things sacrificed to idols, we know that we all have
knowledge. Knowledge makes arrogant, but love edifies. 2 If anyone
supposes that he knows anything, he has not yet known as he ought to
know; 3 but if anyone loves God, he is known by Him.
4 Therefore concerning the eating of things sacrificed to idols, we
know that there is no such thing as an idol in the world, and that
there is no God but one. 5 For even if there are so-called gods whether
in heaven or on earth, as indeed there are many gods and many
lords, 6 yet for us there is but one God, the Father, from whom are all
things and we exist for Him; and one Lord, Jesus Christ, by whom are
all things, and we exist through Him.
7 However not all men have this knowledge; but some, being accustomed
to the idol until now, eat food as if it were sacrificed to an idol;
and their conscience being weak is defiled. 8 But food will not commend
us to God; we are neither the worse if we do not eat, nor the better
if we do eat. 9 But take care that this liberty of yours does not
somehow become a stumbling block to the weak. 10 For if someone sees
you, who have knowledge, dining in an idol’s temple, will not his
conscience, if he is weak, be strengthened to eat things sacrificed to
idols? 11 For through your knowledge he who is weak is ruined, the
brother for whose sake Christ died. 12 And so, by sinning against the
brethren and wounding their conscience when it is weak, you sin
against Christ. 13 Therefore, if food causes my brother to stumble, I
will never eat meat again, so that I will not cause my brother to
Another possible answer is that the logic and decision recorded in Acts 15 isn't inspired, but is simply an accurate recording of James' own thoughts on the issue. This would not negate the doctrine of inspiration of the Scriptures, as explained next.
This surrounding text makes this a very plausible suggestion, and it's not the only place in Scripture where someone's words and advice are recorded, and in the context it's clear that the advice isn't the direct commandment of God, but the opinion of the author. See this previous question for an example.
There are literally hundreds of places in Scripture where one person or another says something that is not the direct word of God. It's just recording the historical events. After all, some of Nebuchadnezzar's orders are recorded, but we don't take those as the Word of God. We have to examine the context, and in this passage, the context could certainly be read that this is just James speaking his opinion and explaining why he holds the opinion.
As with the other question you posted in this vein, it seems odd that this would come from a Jewish perspective. After all, the Old Testament has a similar "contradiction" on whether certain types of food are or are not allowed, a contradiction which is just as easily shown to be a non-issue.