I'm sorry, but no professing Christian has a RIGHT to the Lord's Supper. Hear me? NO RIGHT to it.
You don't even have a RIGHT to preaching, or to baptism--if by "right" you mean access on your own terms. That's the definition of "right," and rights are typically granted by a higher authority--unless there is NO higher authority.
The family analogy is perfectly apt. My children do not have "rights" to the privileges of my house. They do not have a "right" to the refrigerator, a "right" to the car keys, a "right" to education.
There is a just argument that they have some "rights" granted them by God, which their Mother and I are supposed to respect and in some cases provide for (according to our wisdom and judgment). Those "rights" are supposed to mediated to those children through the authority structure of this house. They enjoy those "rights" through the parents.
The principle of "appeal" (to higher authority) is the mechanism by which lesser authority is held accountable for its activity in mediating the rights of subordinates. But anyone who thinks that he's ONLY accountable to God will be disturbed to find that God is displeased with wholesale disregard for the forms He established. There is such thing as "abuse of authority," but such abuse is no license to disparage authority.
I exercise discipline in my house by FEEDING my children: "Come and eat, NOW." By EDUCATING my children: "2+2=4, memorize it" "i before e except after c, your answer is wrong" "did you read your history assignment? good job." By TAKING THEM to church, to grandma's, to the eye doctor, AND to the woodshed.
Discipline is not merely PUNISHMENT! It is the LIFE of the church. Receiving Baptism and the Lord's Supper are BENEFITS of belonging to Christ. So is sitting under Gospel ministry. All the blessings of discipline are just as much a free gift of God as a new heart.
No sensible church will turn away people from hearing the gospel, from hearing the Bible preached in fullness. Because that is the DOOR to heart-submission to God in every area. They should open that venue to ALL, and not just to members.
And they should be sensible about admitting members of the church-universal to their own table, but they may set their own rules as to the manner they will allow it. But it is out of the question that someone who CANNOT BE EXCOMMUNICATED (by any body) should be IN-COMMUNICATED, that is, permitted to the Table.
A half-moment's reflection should be sufficient to make this perfectly clear. That man is his OWN BOSS. his own authority. OK fine, then he can get his own Lord's Supper from himself, or from Christ himself. After all, he doesn't need anything mediated to him, so he can just find a church without any standards, or one that has no idea they will be held accountable by Christ for the care they exercised in these matters.
The point, as far as an unpersuaded Baptist holding membership in a Presbyterian church goes--he is a sinner, and his mind (to our way of thinking) needs sanctification in this area. Shall we punitively discipline a member who tells us "I am having trouble getting my head around the idea of Limited Atonement"?
Admonish him? Scold him? Keep him from the Table? Why?! He needs to keep coming, and have a teachable spirit. He needs to "believe that he may understand."
Obviously, if a man cannot be persuaded of a church's doctrine or practice, if he's hardened to it, then he cannot become a member. Or he needs to find another church, to which authority he can honestly submit. But a man in error should listen in the congregation. He should be submissive to the loving, patient, parent-like care of a church's minister and elders.