Each epistle written to a local church was different. Each had different problems. Each church was different.So where in scripture does it say directly that The Lord's Supper and who it is administered to is a matter of soul-liberty?
Likewise each church that Christ addressed in Revelation 2 and 3 was different one from another. He praised them for their good and condemned them for their error. They were different one from the other. They were not clones of each other. (contradicting RCC teaching). They had their own autonomy and independence, and thus their own soul liberty.
Just as every local church must decide on what standard of music they are going to adhere to, what standard of dress they will impose on members or leadership, if grape juice or actual wine will be used, or even if drinking of alcoholic beverages is right or wrong.
Each church must also decide if their communion is closed, close, or open.
Closed: Only the baptized members of the church may partake.
close: Only members of churches of like faith and order may partake (almost always must be baptized).
Open: Open to any believer
Most of the churches I have been in practice "close" communion: where churches of like faith and order may partake. They must be baptized. Why? Because a person who refuses to be baptized is living in a state of continual rebellion against God. Baptism is the first step of obedience in the Christian life. As long as you will not be baptized you are disobeying God.
What happens when we partake of the Lord's Supper?
Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord.
28 But let a man examine himself, and so let him eat of that bread, and drink of that cup.
29 For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body.
30 For this cause many are weak and sickly among you, and many sleep. (1 Corinthians 11:27-30)
The warning is there in verse 28. Examine yourself. If you are guilty of any sin do not partake, and that includes not being baptized. The church at Corinth were abusing the Lord's Supper. The Lord judged them. The judgment, according to verse 30, resulted in some being weak, some being sick, and some being dead!
This is one of the most important services of the church. It is not to be treated lightly.