The teaching that certain laws are just for Jews is the way many side step the issue..
Look at Acts 15. The apostles were Jews. They had been circumcised. They tried to keep the law of Moses. They had been trying to. If someone wanted to circumcise Gentiles and command them to keep the law of Moses nowadays, most Christians would reject the idea and not want to convene a meeting of the apostles and elders. But the issue then was what to do with the Gentiles?
These Jewish Christians grew up keeping the law, trying to. They grew up in Judaism. They knew from Judaism, from the Old Testament, that God gave the law to Israel. They had commandments. They were to be distinct from the nations. The nations were supposed to be blessed through Abraham. There were prophecies about Gentiles believing the Messiah. But in Judaism, as they would clarify later, they could see that there were certain things that were indicated to be sins for Gentiles. Gentiles were descended also from Noah who had a covenant with God, who had given creeping things for Noah to eat but not the blood (I suppose how much more the higher forms of meat.) Gentiles were kicked out of the land because of sexual immorality, which Leviticus 18 is specific about, and child sacrifice to their gods. And God made everyone. God would inherit the nations. He promised the nations to the Messiah for the asking.
Do the Gentiles have to relate to God through the covenant they grew up under, the law of Moses? Should they be circumcised to keep all these obligations, or not? Do they have to stop eating pork, keep the sabbath the way Jews do, not wear mixed fibers, not cut their hair a certain way, take baths after menstruation and ejaculation or touching a dead body? Do they have to sacrifice in the temple?
Paul participated in the temple. His sins were forgiven through Christ. But he made some kind of vow and shaved his head. He went into the temple with men who had a vow on them and paid their expenses. Peter and John spent time in the temple. At the time, they might have had to do a Jewish ritual, a mikveh/bath/(maybe 'baptism'), and change his clothes, to get in.
Peter had been concerned about going into a Gentiles house. There had been 18 decrees about Gentiles, either the Shammai Pharisees or the Sanhedrin under their leadership (my fuzzy memory or unclear in history, not sure.) Maybe the law Peter was concerned with had something to do with that.
Paul pointed out Titus was not compelled to be circumcised when he went to Jerusalem. But Paul circumcised Timothy the son of Jewish mother. Paul warned the Galatians, presumably predominantly Gentile readers, that if they be circumcised, they had fallen from grace. He did not want them to take on the obligation to follow the whole law. He wanted them to be justified by faith, 'as the just shall live by faith', not attempting to be justified by keeping the law along the lines of 'he that doeth these things shall live by them."
In I Corinthians 7, we see Paul's wish that people walk in whatever state they were called, with an exception for slavery. He wished the circumcised not to seek to become uncircumcised and the uncircumcised not to become circumcised.
I do not see where the apostles in Acts 15 talks about the 'moral law' and 'ceremonial law.'
The moral laws have not stopped and Jesus made that clear.
If it's just theologians or book-authors taking laws here and there and seeking justification to put them into their two categories, maybe it's helpful somehow. But is it Biblical doctrine?
I'd rather understand scripture by understanding the actual teaching of the apostles, the points being made through narrative texts, understanding the specific teachings of Christ, and seeing what God revealed in the Old Testament through narrative, poetry, prophetic declarations, etc.