In Isaiah 65:4, we're told that those who eat the flesh of pigs will go to destruction. Doesn't this apply to Christians?
The biblical prohibition against eating pork is found only in the Law of Moses, and therefore it was only required for the Jewish people. Christians (and Gentiles in general) are not under the Mosaic Covenant, and therefore we are not bound by those restrictions. Therefore, a Christian may eat any food, including pork.
In Isaiah 65:4, the Lord speaks to Israel saying:
Is. 65:1 “I permitted Myself to be sought by those who did not ask for Me;
I permitted Myself to be found by those who did not seek Me.
I said, ‘Here am I, here am I,’
To a nation which did not call on My name.
Is. 65:2 “I have spread out My hands all day long to a rebellious people,
Who walk in the way which is not good, following their own thoughts,
Is. 65:3 A people who continually provoke Me to My face,
Offering sacrifices in gardens and burning incense on bricks;
Is. 65:4 Who sit among graves and spend the night in secret places;
Who eat swine’s flesh,
And the broth of unclean meat is in their pots.
Is. 65:5 “Who say, ‘Keep to yourself, do not come near me,
For I am holier than you!’
These are smoke in My nostrils,
A fire that burns all the day.
Is. 65:6 “Behold, it is written before Me,
I will not keep silent, but I will repay;
I will even repay into their bosom,
Is. 65:7 Both their own iniquities and the iniquities of their fathers together,” says the LORD.
“Because they have burned incense on the mountains
And scorned Me on the hills,
Therefore I will measure their former work into their bosom.”
In this passage, the Lord cites numerous examples of how Israel has disobeyed the instructions given to them in the covenant of Law, including Israel's disobedience of the law commanding Israel not to eat pork. The people of Israel were commanded in their law to never eat pork, but the nation disobeyed the Lord nonetheless. Because of their disobedience under the Law, the Lord promises to prevent them from receiving their Messiah for a time, while the Gospel goes to the Gentiles.
The Old Covenant was only binding on Israel. It was intended to set Israel apart from the Gentile world, and it eventually gave the Lord just cause to withhold the Kingdom from Israel while offering salvation to the Gentiles. The Lord was speaking to Israel in 65:4, so His admonishment was directed to Jews alone, who were willingly violating the Old Covenant law.
Today, Christian believers in Jesus Christ are saved by the grace found in the New Covenant, and as Paul taught, we are not bound by the regulations of the Law found in the Old Covenant:
Rom. 6:14 For sin shall not be master over you, for you are not under law but under grace.
Rom. 7:4 Therefore, my brethren, you also were made to die to the Law through the body of Christ, so that you might be joined to another, to Him who was raised from the dead, in order that we might bear fruit for God.
Rom. 7:6 But now we have been released from the Law, having died to that by which we were bound, so that we serve in newness of the Spirit and not in oldness of the letter.
Col. 2:16 Therefore no one is to act as your judge in regard to food or drink or in respect to a festival or a new moon or a Sabbath day —
Col. 2:17 things which are a mere shadow of what is to come; but the substance belongs to Christ.
Therefore, any Gentile and all Christians are free to consume pork or anything God has made, since the regulations of the Law do not apply to those who are not bound by that covenant. Only unbelieving Israel is bound by that covenant today.
Furthermore, there is nothing inherently sinful about pork or any food. The Lord's displeasure at Israel for eating pork had nothing to do with pork itself. Just as the fruit from the Tree of the Knowledge of Good and Evil in the Garden was not inherently sinful, neither is pork inherently sinful. In both cases, the problem wasn't the food itself, for as Paul says:
1Tim. 4:4 For everything created by God is good, and nothing is to be rejected if it is received with gratitude;
1Tim. 4:5 for it is sanctified by means of the word of God and prayer.
Rather, the problem in both cases was disobedience to God's word. Adam received an instruction from God, which he disobeyed resulting in God's judgment against him. Likewise, Israel received a word to abstain from pork in the covenant, yet they disobeyed, provoking His anger against them.
For more information on this issue, we invite you to read the following articles on the believer's relationship to the Law of Moses.