Calvinists have something called the regulative principle.
That depends on our definition of
Calvinists. What the word seems to have come to mean is someone who believes in Reformed soteriology, i.e. the Doctrines of Grace or Five Points. If we're working from that definition, then it would be correct to point out that while Steve Schlissel, David Chilton, and James Jordan are/were all "Calvinists," they have either completely denied the regulative principle or revised the traditional understanding of it to such an extent that it is no longer distinctively Reformed.
However, it seems to me that the problem with such an idea is that the very detailed regulations regarding public worship in the Old Testament are completely missing in the New Testament. If God wished to regulate Christian worship in the way Calvinists seem to imagine, why are those detailed regulations missing from the New Testament?
As someone who believes that the regulative principle excludes the singing of uninspired hymns, instrumental accompaniment, and the celebration of extrabiblical holy-days (not all "Calvinists" agree with that position, mind you), the way that I would answer your question is to say what you see as the "problem" for the regulative principle is something that forms its main insight: the detailed regulations are missing because God desires a very simple form of worship in the New Covenant.
In the Old Testament, public worship is heavily tied to the tabernacle and later to the temple. The author of the letter to the Hebrews informs us that the ceremonies related to the temple served "as a copy and shadow of the heavenly things" (Heb. 8:5), and were made after the pattern of the heavenly things shown to Moses on Mt. Horeb. Paul tells us that the holy-days of the Jewish calendar, which are described in detail in Lev. 23, were "a shadow of the things to come, but the substance belongs to Christ" (Col. 2:17), and he gives the Corinthian church a specific example: "For Christ, our Passover lamb, has been sacrificed. Let us therefore celebrate the festival, not with the old leaven, the leaven of malice and evil, but with the unleavened bread of sincerity and truth" (1Cor. 5:7-8). All of these old ceremonies that served as weak shadows to teach the Jewish church, the author of Hebrews says, are passed away (e.g., Heb. 7:18-19).
What we say, then, in relation to the regulative principle, is that God has not given very detailed regulations about, e.g., how the cup and table in the Lord's supper should be constructed, or how our places of worship should be decorated, or when we should meet on the Lord's Day, because He wishes to make it clear that we have the substance of justification and sanctification, not just the types and shadows.
An example of where this understanding of the ceremonial law meets with the regulative principle is in a cappella singing. Historically, the Reformed churches recognized that the use of musical instruments in worship is confined in the Bible to temple-worship. (Yes, we see the practice of women dancing with tambourines as a civil act of celebration, but there is never the suggestion that this is normative for the formal public worship of God.) It is the Levite men who use the instruments, during the sacrifice, in the public worship of God. And so, the Reformed argument was that, since instruments seemed to be ceremonial and are not renewed in the New Testament, they are excluded by the regulative principle, and with good reason: musical instruments were only a type and shadow of the emotions of joy and hope that are to be found in the believer's heart. We of the New Covenant concentrate on the substance when we "address one another in psalms, hymns, and spiritual songs,
singing and making melody to the Lord with our hearts" (Eph. 5:19). (And I think that a cappella singing is a key example from the Reformed churches, because John Calvin himself argued for a cappella singing and cited Augustine as precedence.)
This is one reason why, historically, Reformed worship has been very simple. In times past, it was unusual to see a Reformed church with ornate decorations in it, or with an extensive liturgy and calendar. We no longer need those things, for the most part. God has left us with the sacraments as visible signs and seals of His grace, and He has left us with the Lord's Day as our only remaining holy-day that represents to us our final Sabbath in the resurrection, but in the New Covenant He has given us little else to visually illustrate His doctrines to us. And this is not a problem for us. For us, this is the way God intended for us to worship as we anticipate Christ's return.
(All quotations of Scripture are from the ESV.)
