The preceding events: The 1st Book of Moses (Genesis), 1,29 says: Then God said, "I give You every seed-bearing plant on the face of the whole earth, and every tree that has fruit with seed in it. They will be yours for food". This corresponds to the insight that man has mainly the teeth and digestive organs of a "fruitarian" being - eating fruits - (and not "omnivorous" - eating everything - as one might think, if one only knows the categories of animals "eating meat", "eating everything" and "eating grass").
However, after the Flood - archeologically known, e.g. in the middle-east - (Genesis 9,3-4) to Noe: "Everything that lives and moves will be food for you; ... But you must not eat meat that has its lifeblood still in it." Up to here everything relates to an era before that of today; so it did not only concern the later Jews - presuming it has been handed down correctly.
After the exodus from Egypt it became acknowledged and further details were added in the 5th Book of Moses (Deuteronomy)14,3-21. It seemsthat after the flood, the principle was to allow everything and to exclude only the most unsuited foods. Some of these points can be found in dietetics too. Nevertheless, there were still cases in which the special value of vegetable food was stressed - without any binding regulations , see Daniel 1,8.

There often seemed to be a relationship between the many extensive rules concerning sacrifices and the eating of sacrificed meat - which is hard to understand today. The Prophet Hosea (6.6) already passed on the message: "I desire mercy, not sacrifice - and recognition of God rather than burnt offerings." With reference to this passage, Jesus said: "But go and learn what it means: ' I desire mercy, not sacrifice'" (Matthew 9,13 and 12,7). Concerning Luke 22,11, where Jesus asks, where he may eat the Passover (meat) – which does not occur during the following Last Supper at all - there are early Christian "apocryphal" scriptures (which were not included in the biblical canon around 400 after Christ) like the "Gospel of the Ebioneans". Here he says, answering: "Would I happen to desire to eat meat (of a lamb) with you this Passover?" The Aramaic language used fewer words for sentences like this, thus allowing various interpretations if the original intonation was not known. This led to various translations, destined to conflict with each other.
The former Judeo-Christian communities - later most of them were islamized - were a true part of Early Christianity; in spite of the fact, that there were some differences between them and other developing churches.

Acts 15,19 reports the judgement of Jacob, leading the Early Community, that "We should not make it difficult for the Gentiles who turn to God (taught by Paul). Instead we should write to them, only telling them to abstain from food polluted by idols, from sexual immorality, from the meat of strangled animals and from blood." But the early church's historian Eusebius, and apocryphal Apostles' acts and so on lead to the view, that Jesus, John, Peter, Jacobus ...  themselves usually lived without meat.
According to Matthew 15,11-20  and Mark 7, 17-21 Jesus stressed more "things that come out of the mouth", than "whatever enters the mouth"; however this was more related to questions of Pharisees concerning washing the hands before eating. The same relation of values is given in Jesus' wording about the "beam in one's own eye" and the "splinter in the eye of someone else". That means, it is better to start with one's own weak points, instead of with the fear of influences from outside. Anyway, the said passage does not say that one must eat meat.
In Luke 10,8 Jesus recommended the disciples to eat whatever is offered by their hosts during their travels. That does not automatically mean that this is an indifferent question. Still today, e.g. in the Arabic countries, a guest refusing offered food or drinks can produce the most incalculable reactions if he/she is not very skilled. Furthermore, the original disciples had been given the special ability not to be harmed by even very harmful substances (Mark 16,18.). So it is of no use to generalize about such bible quotes without limits outside of the context.