There are parts of the Bible that are there for "faith" and parts that are there for "life". The "unclean food" was because for long parts of human history eating certain foods had a high likelihood you were going to die.

Old Testament God didn't care about pigs or shellfish, but a law against them was created because it saved lives.

Later, when those foods were no longer dangerous, they tried to get rid of the law forbidding it, but since they had used God as the excuse the first time, people pushed back.

It's possible that Jesus said those things about those foods, but it's also possible that the Church added them in the 100-200 years after Jesus before the Bible was written.

The point of "divine inspiration" is not that everything in the Bible happened as described, but that it exists (or existed) for a good reason. The difficulty sometimes is determining what is or is not necessary.

A good example there is tattoos. Back in the day, people got a tattoo, it got infected, they died. Thus the Lord says: no tattoos. Today, getting a tattoo is pretty safe in most places. Should we allow tattoos? Probably? But "my body is a temple"... sure, most temples have images and artwork that glorify God, so why not decorate your temple in His name?

I don't have tattoos and don't plan to, but it's a good example of the gray area and original cause/effect intention for these rules.