What is the biblical basis for the theory that Christians should not eat pork?

In the Judeo-Christian tradition, the biblical basis for dietary restrictions (and let's not forget dietary permissions, too!) is spiritual in nature. Just as in the moral and ethical realms there are restrictions such as those outlined in the Ten Commandments, so also in the practical and day-to-day living out of one’s faith—whether Jew or Gentile, there are both biblical restrictions and biblical permissions.

The restrictions in particular have both “spiritual” and “physical” ramifications, since people who are created in the image of God are not just spiritual creatures but a somewhat mysterious nexus of the spiritual and the material, mind and matter, soul and body.

The restrictions can also be very practical in nature, and in the early history of Israel as a nation they cover such things as the treatment of servants; the lending of money; various sexual do’s and don’ts; the treatment of strangers; the care of animals; contracts; bodily functions; the treatment of skin diseases; and the list goes on and on. The Old Testament books of Exodus and Leviticus are filled with teachings and protocols on such practical issues.

A key “Old Testament” concept concerns the distinction between clean and unclean. Again, those antonyms (viz., clean and unclean) have both physical and spiritual components and applications. Levitical priests, for example, could contaminate themselves by coming into contact with a dead person or a dead animal. In other words, they became, for a time, unclean. God, however, provided a protocol for the priest to be cleansed from his uncleanness and then become fit once again to represent God to the people.

All this to say, the Old Testament teaching about what foods were clean and what foods were unclean was highly practical. More important than practicality, however, was that 1) the teaching came from God, and he, above all, was to be obeyed and was worthy of Israel’s obedience; and 2) the rules by which the children of Israel were to live were designed to make them different, in a good sense, from people in the nations surrounding them. These nations and people groups, by and large, did not worship the one true God of the Israelites: YHWH (the LORD).

On the contrary, they worshiped many gods, and quite often that “worship” of their gods and idols involved not only superstition, myths, and evil practices, but it tended to contribute to the moral decay of their nations. Just as Christians today are to be "salt" and "light" in a corrupt and spiritually dark world, so too were the children of Israel to be a beacon of light in the midst of the cultural decay of their time.

In conclusion, Jesus’ teaching and the teaching of the apostles and writers of the New Testament is very clear: All foods are clean, and they may be eaten with thanksgiving toward God if they are eaten in faith and with a good conscience (see, for example, Mark 7:19; Romans Chapters 14 and 15; and 1 Timothy 6:17).

If, however, a Christian has a “hang-up” about eating something in particular, and his or her brother or sister in Christ does not have a similar “hang-up,” then neither of them is to judge each other for either eating or not eating. Why? Because 1) only God, ultimately, is fit to judge people in matters of conscience; and 2) to judge or condemn others regarding matters of conscience is to violate the law of love.

Answers to original question before the Nov 21 edit:

What is the biblical basis for the theory that Christians should not eat pork?

It is based on a law in the Old Covenant, and ignoring or rejecting the idea that the New Covenant overrides that law.

Are Christianity and Islam similar in their teachings regarding dietary restrictions and prohibitions, or are their teachings different?

Different.

Why is my upbringing as a Christian at odds with the teachings of Islam?

They are extremely different religions with very little in common. Some even argue quite well that they are exact opposite religions.

How can two religions like Christianity and Islam be so different regarding this issue?

They are very different religions overall, so it should not be surprising they are different in this specific regard.

I would like to be able to provide people with logical reasons for my beliefs, including my belief that it is OK to eat pork.

In most social situations, this is simply a matter of saying "I'm Christian, not Muslim" and that will make sense to everyone around you.

Answer to the Nov 21 edit of the question:

I've been tormented by hearing from friends and such (that aren't religious) that they've heard and been told eating pork and chicken is a sin. And that it means going to hell....which is obviously out of proportion. Was it haters? Or people against Christianity totally? Or what?

That is really hard to answer without knowing those people. You say they are not religious. That would indicate that they are probably not well informed about religious things, and just repeating things they heard from random unreliable sources. That is why this web site exists, for people like them. Hopefully they will find it and learn from it.

The Scriptural basis for the Jewish diatary laws is Leviticus 11. In particular, verse 7 says:

And the swine, though he divide the hoof, and be clovenfooted, yet he cheweth not the cud; he [is] unclean to you.

(This and all following quotes are taken from King James Version, for consistency.)

These admonitions are repeated in Deuteronomy 14; particularly, verse 8 says:

And the swine, because it divideth the hoof, yet cheweth not the cud, it [is] unclean unto you: ye shall not eat of their flesh, nor touch their dead carcase.

This is all well and good, but up until here we are talking of the Old Testament and Mosaic Law. Coming into the New Testament, the Evangelists (Matthew 15:1–20, Mark 7:1–23 and Luke 11:37–41) report Jesus' words:

Not that which goeth into the mouth defileth a man; but that which cometh out of the mouth, this defileth a man.

Of course, in this case it was an issue of the disciples not washing themselves before eating bread, but it establishes the precedent for the question described in Acts 15, which has been described as the first Ecumenical Council, or the Council of Jerusalem:

1. And certain men which came down from Judaea taught the brethren, [and said], Except ye be circumcised after the manner of Moses, ye cannot be saved.
2. When therefore Paul and Barnabas had no small dissension and disputation with them, they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question.

(...)

6. And the apostles and elders came together for to consider of this matter.
7. And when there had been much disputing, Peter rose up, and said unto them, Men [and] brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe.

(...)

19. Wherefore my sentence is, that we trouble not them, which from among the Gentiles are turned to God:
20. But that we write unto them, that they abstain from pollutions of idols, and [from] fornication, and [from] things strangled, and [from] blood.

These abstinences referred to in verse 20 are the so-called Noahide Laws, which are required of all the sons of Noah, i.e., everybody, since all men who were not sons of Noah perished in the Flood. Therefore, there is a sound Scriptural basis to argue that Christians are specifically allowed to eat pork.

That being said, there is nothing that prevents a Christian from deciding to follow these laws anyway (as Paul himself did, check Acts 21:26). This gives rise to the so-called Jewish Christianity, who are Christians who confess the divinity of the Christ while at the same time keeping the 613 Jewish mitzvot.

Finally, I think that your Muslim friends' reactions are probably due to a misconception that Jews and Christians are bound to their halal dietary laws, or that they consider that anyone who violates the commandments given to them in the Quran and/or the Sunnah are going to earn eternal condemnation, regardless of whether or not they ever converted to Islam in the first place.