What are the 'things' offered to idols? In days of old, the leaders of different communities would make for themselves statues of creatures, then to obtain obedience from the general population, they would threaten that the creature would kill them or devour them if they did not work as expected. To continue with the illusion, feasts were assembled and pagan priests would do what they could to make it appear that the statue was eating. Or sacrifices where made, to make the illusion appear that the statue killed someone.
Acts 15:29 NKJV
that you abstain from things offered to idols, from blood, from things strangled, and from sexual immorality. If you keep yourselves from these, you will do well.
The main point is that by eating of the things offered to idols, you would stand as a affidavit witnessing that the events of the illusion where true. They obviously are not true. So standing in any form of position to help conclude this illusion was real was supporting a lie.
Acts 15:20 NKJV
but that we write to them to abstain from things polluted by idols, from sexual immorality, from things strangled, and from blood.
Now knowing above, If I where to abstain from eating the meat, but was part of the ceremony , and made some elaborate display for them like presenting the knife, or playing a trumpet. This still all would fall under helping to conclude this illusion was real and supporting a lie.
To understand How was this understood by the Apostles I assume it was given to them by God's Holy Spirit either supernaturally, or as a common truth.
They wrote this letter by them: The apostles, the elders, and the brethren, To the brethren who are of the Gentiles in Antioch, Syria, and Cilicia: Greetings.
To understand how their followers perceived it. I guess here, but I would assume that they have witnessed such gatherings and displays due to the location. I do not know at this moment about what idols where being sacrificed to in Antioch, Syria, or Cilicia. I feel it safe to say though that the command would have been elaborated on if not to be naturally understood by the audience of that time.
This 'rule' is based on the Second Commandment of the Ten Commandments the Old Testament law. According to the Hebrew OT: Westminster Leningrad Codex, Hebrew OT: WLC (Consonants Only), and also the Septuagint.
Exodus 20:4-6 NKJV
“You shall not make for yourself a carved image—any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; 5 you shall not bow down to them nor serve them. For I, the Lord your God, am a jealous God, visiting the iniquity of the fathers upon the children to the third and fourth generations of those who hate Me, 6 but showing mercy to thousands, to those who love Me and keep My commandments.
Can Sunday be a religious day for Christians if it was already a religious day offered to the pagan sun god? Yes. Not for the purpose of raising the pagan sun god to honor. Yet God explains through Paul.
In Hebrews 3:7-11 we are directed to understand Psalm 95:7–11.
Psalm 95:7–11 NKJV
For He is our God, And we are the people of His pasture, And the sheep of His hand. Today, if you will hear His voice: 8 “Do not harden your hearts, as in the rebellion,
As in the day of trial in the wilderness, 9 When your fathers tested Me; They tried Me, though they saw My work. 10 For forty years I was grieved with that generation,
And said, ‘It is a people who go astray in their hearts, And they do not know My ways.’
11 So I swore in My wrath, ‘They shall not enter My rest.’”
So in the fullness of Hebrews Chapter 3 he concludes that the rest was no longer available to them because of their unbelief.
Hebrews 3:19 NKJV
So we see that they could not enter in because of unbelief.
Then in Hebrews Chapter 4 he points out that a new day has been created to enter into rest.
Hebrews 4:7 NKJV
again He designates a certain day, saying in David, “Today,” after such a long time, as it has been said: “Today, if you will hear His voice, Do not harden your hearts.”
The need for this is pointed out
Hebrews 4:8 NKJV
For if Joshua had given them rest, then He would not afterward have spoken of another day.
Going back to point out that the day was to continuously be today.
Hebrews 3:13 NKJV
but exhort one another daily, while it is called “Today,” lest any of you be hardened through the deceitfulness of sin.
Therefore here is logic. If today you enter into his rest, and continually enter into his rest for every today. Then all the Sabbath days would then be covered, so the fulfillment of the duty to honor the seventh day would always be completed. Also since when today happens also to be a Sunday. That day is also considered a "Today". Therefore the festival may continue for any day that becomes today!
So then know in case this is your situation. If you do happen to know a Pagan Sun Worshiper I say be careful not to include yourself in any of the duties, or offer respect that supports any illusion. But instead love them and show them the perfect way. Amen.