The author didn’t mention what specifically the vows were. Was one of them to profess belief in the Westminster Confessions, or is that not required?
To be an elder or a deacon, yes but to be a member of the church, no. At least that is how it works in the Presbyterian Church in America. I assume the OPC works in a similar fashion.
Not in most Baptist Churches. In most Baptist Churches a profession of faith and Baptism as a believer is what is required. Does the RCC require an oath of loyalty to it?
This is what the person vows in the PCA:
(All of) you being here present to make a public
profession of faith, are to assent to the following declarations and
promises, by which you enter into a solemn covenant with God
and His Church.
1. Do you acknowledge yourselves to be sinners in the sight of
God, justly deserving His displeasure, and without hope save
in His sovereign mercy?
2. Do you believe in the Lord Jesus Christ as the Son of God,
and Savior of sinners, and do you receive and rest upon Him
alone for salvation as He is offered in the Gospel?
3. Do you now resolve and promise, in humble reliance upon
the grace of the Holy Spirit, that you will endeavor to live as
becomes the followers of Christ?
4. Do you promise to support the Church in its worship and
work to the best of your ability?
5. Do you submit yourselves to the government and discipline
of the Church, and promise to study its purity and peace?