QUICK ANSWER: At Acts 15:19 they only named a few important commandments because they knew that the gentiles turning their heart to the Father would learn about the other things on the 7th day Sabbath of YHWH, because the Law was taught every 7th day Sabbath in the synagogues/congregations.
Concerning "the law for Christians" part they may teach, it's completely made up, nothing like that is said here, and it's not found anywhere inside of the Bible, and does not even fit to the context of Acts 15:19 but is actually contradicted by Acts 15 if you are understanding what you are reading.
There are a few misconceptions from Acts 15:19.
From this passage, some men are claiming that the few commandments named here are the only commandments that we have to obey now, even though the Messiah himself plainly told us to obey them all and to not neglect even the smallest thing.
Also, they're saying it's part of "the law for Christians", though they're completely making this up because it's not something that comes from the Bible, and Christians do not have a new or separate law, there is only 1 Law for all of mankind.
Men may make such claims of this is "the law for Christians" with other verses as well, and those areas as well are covered in the misconceptions, for example, such as the page titled "Love" where men twist a verse to try and say all we have to do now is "love", and leave out the fact the verse even says we must keep the entire Law to love, but people listen to those men rather than the Messiah for what he really is saying.
At Acts 15, they are writing a letter to gentiles who are new to the faith, and they decide to only name a few commandments to them in their letter, however, the reason why more commandments were not given to them is stated in the passage, and people seem to be choosing to ignore that part.
Here is the text;
Acts 15:19 "Therefore my judgment is that we should not trouble those of the foreigners who turn to Elohim, but should write to them to abstain from the things polluted by idols, and from whoredom, and from what has been strangled, and from blood, for from ancient generations Moses has had in every city those who proclaim him, for he is read every Sabbath in the synagogues"
The text when read in context states they only gave those commandments because the Law is taught every 7th day Sabbath of YHWH in the synagogues(buildings for congregating), so those people who were repenting from false elohim and idol worship, and beginning to serve YHWH the one true Elohim, would be taught the Law when they listened to the words of Moses.
(Hopefully you know already that Moses was the one whom YHWH gave his Law through. YHWH spoke to Moses and then Moses spoke to YHWH's people because they didn't want to hear YHWH's voice any longer, because it terrified them!
If you're not aware of this, then you may indeed fail to realize they're actually saying here that the entire Law is taught every week on the 7th day Sabbath.
Also notice, they're talking about the 7th day Sabbath here and it looks like they're expecting people to still be observing it and not saying it has been abolished.)
The Messiah, Paul, and the 12 disciples, were not teaching us a doctrine to replace the eternal Law of YHWH, men who claim such are lying, and the Bible never says anything close to such a thing.
It always refers to THE Law, that is, the Law of YHWH given through Moses.
The disciples were focused on spreading to the ends of the Earth the good news(Gospel), The kingdom of YHWH is coming soon and we have received Salvation from YHWH through his son Yahushua the Messiah and we have been cleansed.
They showed at Acts 15 they intended for the people to come to the Word of YHWH and learn the requirements and will of YHWH.
Compare that to the modern Christian denomination, they do not teach these scriptures, and use their power to prevent new members from learning from Moses.
So they were only teaching some basic, important commandments, much like I did on the "How to get Saved" page in case someone read the page and was totally new, not knowing any of the commandments yet.
The commandments I shared was not the entire Law, but I intended for everyone reading my post there to seek YHWH themselves and hear his Word.
It's not easy to write out the entire Law of YHWH in a short simple letter, or in a brief time frame, but if you simply tell a gentile or newcomer who has never been taught anything about YHWH's Word to Love, then that covers an entire multitude of the commandments, since if they love their neighbor they won't harm them or cheat them or steal anything from them including their life mate.
So please read Acts 15 in context and pay attention to them knowing that the Law and its commandments were taught every Sabbath of YHWH in every city in the synagogues, so the people could learn further on the Sabbath.
People who are just being born into repentance also may need to hear a different teaching than someone who has seen YHWH for themselves, such as Yisrael at Exodus 20:1 when YHWH reveals himself to them.
You have to give them only what they need and nothing more, so their faith is put into Elohim and then they themselves are ready to go on and learn the foundation of being righteous.
If you speak to someone who has just heard of YHWH because their parents hid him from them, and their faith isn't yet solid in him, it could be counter-productive to ignore certain things they need to learn 1st and instead go straight into saying;
"You have to do all of these commandments NOWWW!", and then give them a list of laws before they even know him.
They indeed need to perform righteousness, but they need to reach that part in the proper order for the best outcome.
You don't want to turn them away, and you have to love YHWH before you want to obey him, you have to circumcise your heart.
The gentiles were even from societies where their false religions actually had laws that appealed to the wicked human nature and none or not so many that made you keep yourself from any urge you had, so men probably took all of this into consideration to help ease them into the Truth.
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