Scott Maciver has written a fine article over on the Our Confession website on the consistency of our holding to exclusive Psalmody:
“There are some today who have taken office in a church or are members of a church who would consider themselves to be exclusive psalmists and were we to ask them what their position on worship is; they would confidently assert that it would be that of exclusive psalmody. The test of the genuineness of our position comes when, like those referred to in Macrae’s Diary, we find ourselves in a worship setting out-with our own congregation or denomination where the worship is contrary to unaccompanied exclusive psalmody.
In such a situation, there are two options available to us. Do we continue to uphold the Biblical position we profess which forbids the worshiping of God in any other way not appointed in His Word (Westminster Shorter Catechism, Q51) or do we, when we are in a different setting, adopt a different position on worship all together? The temptation to some may be to partake in worship, no doubt offered in all sincerity, which is contrary to both that which we profess to believe and that which God has commanded in Scripture. Some may, for instance, sing the words of uninspired hymns to avoid giving offence to those sat in the pew next to them or to avoid disrupting the fellowship. Others may find themselves singing as they would consider it better to sing the words than to be silent and to not worship at all. Yet again, others may sing them as they consider the words to be theologically correct. On the other hand do we simply keep silent, not through any sense of superiority to those around us but by a consistent God honouring application of His commandments regarding worship?”
In answer to these questions, Maciver gives the following summary as an answer:
“Now that we have considered these two options open to us, we are left with a number of questions. Is our concern about obeying man before God when Scripture tells us that we ought to obey God rather than men (Acts 5:29)? Are God’s commandments only to be obeyed under certain circumstances and only in particular locations? Is our position on exclusive psalmody simply a preference or is it a conviction that we by God’s grace seek to consistently apply at all times? Finally, can it ever be defensible for an office-bearer who has vowed to exclusive psalmody to preside over public worship where uninspired hymns are being sung?”
These are great questions, I would be very interested in getting your feedback on these issues. For those who contribute to the forum at Our Confession, keep us updated on the discussion.
Exclusive Psalmody 
I was taught from the earliest age that “we” do not sing anything except the Psalms in worship. It boils down to just the word “exclusive”. One is either exclusive in Psalmody or not. Anytime one is worshiping, regardless of setting, the regulative principle is applicable. Some make a distinction between informal and formal aka “in-church” worship. However as we read the second commandment do we see any such distinction? God’s jealousy for His worship is not limited to one or two hours on the Lord’s Day is it?
The requirements of the second commandment to keep pure and entire all such religious worship as God has appointed in His Word, is required of each and every individual. Now the scope of one’s influence is limited by one’s calling and station in life, but each person is responsible to God for his or her own behavior. While we might ourselves be in a position where we have no control of the larger worship service, we always have control over our own lips and tongues.
It can come at a considerable cost to remain silent while the congregation sings their counterfeits, but we must remember that as Maciver pointed out should we obey man or God? Obeying God is worth the cost. For those in position of minister or elder, especially for the minister, the cost is much greater. I’ve known ministers who’ve been basically fired for refusing to preside over the idolatry that the people insist upon, cf. Ex 32.
In the end we must remember what Christ tells us in Psalm 37:
A little that the just man hath
Is more and better far
Than all the wealth of many such
As wholly wicked are.
To any that would object to characterizing those who sing counterfeits in lieu of the Psalms as “wholly wicked”, the Westminster Larger Catechism on the reason annexed to the second commandment says that God is “accounting the breakers of this commandment such as hate him, and threatening to punish them unto divers generations”
The singing of counterfeit psalms is as though all the words to all those counterfeits are nothing more than a refrain of
I am pleased with me myself
I am my own righteousness
God who is the LORD I hate
Christ and his commands I loathe.
Is the above shocking? Sure, but do we really confess that it is an act and attitude of hate by those who break the second commandment which such contempt of God as to approach him with songs of their own making, having laid aside the Songs He himself inspired for us to sing?