Anti-Catholic TAO (The Anonymous One, or "Turretinfan" is aware of it because he critiqued some of this material of mine, and is aware of my response, that prominently mentioned it. But he won't rebuke this notion of deliberately not praying for another human being (because -- I speculate -- she is deemed as wicked and non-elect, and/or unregenerate; hence totally depraved?). John Bugay won't renounce this disgraceful display of supposedly "Christian" piety. Steve Hays, on whose blog this link was posted, has not done so, either. It seems that none of the fringe wing of (active, online) anti-Catholic Calvinists (thus, far, anyway) will denounce or renounce this article or the concept it highlights.
As a bizarre, curious aside, our friend Ron seems quite obsessed with all things sexual, including defense of immoral practices, such as masturbation, which he defends on his second website (that seems to be completely devoted to such things), in a three-part series (one / two / three). Shades of Steve Hays, who has defended the same grave sin (one / two / three) . . . Hays makes sexual jokes about nuns, but Ron takes it a step further, and makes sexual jokes and insults about Mary and Joseph, and writes blasphemy (with explicit sexual detail) about Our Lord Jesus.
Some of his morally ridiculous and scandalous posts, have titles such as: "Lot's Wet Dreams," "The Cult of the Orgasm," "Was Joseph Permitted to Kiss Mary?," "Rez Erection?" (a particularly outlandish and also blasphemous screed), etc. This is a very disturbed person indeed, who has no business writing publicly and representing Christianity of any sort. Where is the oversight? Where is his pastor on this (if he even has one)? Why doesn't the anti-Catholic online community rebuke this and demand that it be removed from view? Let's definitely lift Ron up in prayer, and pray that his anti-Catholic cronies will speak up against this outrageous material, if they become aware of it (after reading this, if not by some other means).
Fundamentalist anti-Catholic Calvinism and self-generated orgasm and Woodstock Free Love: quite a combination there. What would the old Puritans think? Even TAO would blush at such a juvenile display of sinful carnality and sensuality. Will he rebuke it publicly? We'll see, won't we (because he will surely read this). I guess Ron can find nothing better to do with his time than exalt the glories of auto-sexuality and mock people with serious health issues, writing posts urging others to not pray for that person. He really has his Christian priorities straight there, doesn't he?
But back to the topic at hand. In order to refute the notion of deliberately refusing to pray for folks one deems too wicked to deserve it, I brought Holy Scripture to the table (expanded for more context presently):
1 Timothy 2:1-4 (RSV) First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all men,  for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way.  This is good, and it is acceptable in the sight of God our Savior,  who desires all men to be saved and to come to the knowledge of the truth.
Since we're dealing with Calvinists, then it is sensible to see what John Calvin would have to say about this. First, let's look at what Ron Van Brenk, digging in his heels, reiterated today, on TAO's blog:
Now, as I mentioned in the first part of that "Do NOT Pray" series- there are several times when we are commanded NOT to pray for people. And Dave's recourse to 1 Tim. 2:1 does not stand up to proper scrutiny. Will be addressing a response [to] him later tonight on that.
Now, let's see what John Calvin had to say about the matter, from his Commentaries (for 1 Timothy 2:1-4):
That, above all, prayers be made. First, he speaks of public prayers, which he enjoins to be offered, not only for believers, but for all mankind. Some might reason thus with themselves: “Why should we be anxious about the salvation of unbelievers, with whom we have no connection? Is it not enough, if we, who are brethren, pray mutually for our brethren, and recommend to God the whole of his Church? for we have nothing to do with strangers.” This perverse view Paul meets, and enjoins the Ephesians to include in their prayers all men, and not to limit them to the body of the Church.
. . . Paul, in my own opinion, simply enjoins that, whenever public prayers are offered, petitions and supplications should be made for all men, even for those who at present are not at all related to us. And yet this heaping up of words is not superfluous; but Paul appears to me purposely to join together three terms for the same purpose, in order to recommend more warmly, and urge more strongly, earnest and constant prayer. We know now sluggish we are in this religious duty; and therefore we need not wonder if, for the purpose of arousing us to it, the Holy Spirit, by the mouth of Paul, employs various excitements.
And thanksgivings. As to this term, there is no obscurity; for, as he bids us make supplication to God for the salvation of unbelievers, so also to give thanks on account of their prosperity and success. That wonderful goodness which he shews every day, when “he maketh his sun to rise on the good and the bad,” (Matthew 5:45,) is worthy of being praised; and our love of our neighbor ought also to extend to those who are unworthy of it.2 For kings He expressly mentions kings and other magistrates because, more than all others, they might be hated by Christians. All the magistrates who existed at that time were so many sworn enemies of Christ; and therefore this thought might occur to them, that they ought not to pray for those who devoted all their power and all their wealth to fight against the kingdom of Christ, the extension of which is above all things desirable. The apostle meets this difficulty, and expressly enjoins Christians to pray for them also. And, indeed, the depravity of men is not a reason why God’s ordinance should not be loved. Accordingly, seeing that God appointed magistrates and princes for the preservation of mankind, however much they fall short of the divine appointment, still we must not on that account cease to love what belongs to God, and to desire that it may remain in force. That is the reason why believers, in whatever country they live, must not only obey the laws and the government of magistrates, but likewise in their prayers supplicate God for their salvation. Jeremiah said to the Israelites, “Pray for the peace of Babylon, for in their peace ye shall have peace.” (Jeremiah 29:7.) The universal doctrine is this, that we should desire the continuance and peaceful condition of those governments which have been appointed by God.. . . If any one ask, Ought we to pray for kings, from whom we obtain none of these advantages? I answer, the object of our prayer is, that, guided by the Spirit of God, they may begin to impart to us those benefits of which they formerly deprived us. It is our duty, therefore, not only to pray for those who are already worthy, but we must pray to God that he may make bad men good.
Other Calvinists agree. For example, Barnes' Notes (for this passage):
For all men. Prayers should be made for all men--for all need the grace and mercy of God; thanks should be rendered for all, for all may be saved. Does not this direction imply that Christ died for all mankind? How could we give thanks in their behalf if there were no mercy for them, and no way had been provided by which they could be saved? It may be observed here, that the direction to pray and to give thanks for all men, showed the large and catholic nature of Christianity. It was opposed entirely to the narrow and bigoted feelings of the Jews, who regarded the whole Gentile world as excluded from covenant mercies, and as having no offer of life. Christianity threw down all these barriers, and all men are on a level; and since Christ has died for all, there is ample ground for thanksgiving and praise in behalf of the whole human race.
Likewise, John Gill:
not only for all the saints, for all the churches of Christ, and, ministers of the Gospel; nor only for near relations and friends, according to the flesh; but for all the inhabitants of the country and city in which men dwell, the peace and prosperity of which are to be prayed for; yea, for enemies, and such as reproach, persecute, and despitefully use the saints, even for all sorts of men, Jews and Gentiles, rich and poor, high and low, bond and free, good men and bad men:
And the 1599 Geneva Study Bible:
Having dispatched those things which pertain to doctrine, he speaks now in the second place of the other part of the ministry of the word, that is, of public prayers. And first of all, answering the question for whom we ought to pray, he teaches that we must pray for all men, and especially for every type of magistrate. And this thing was at that time somewhat doubted of, seeing that kings, indeed, and most of the magistrates, were at that time enemies of the Church.
And Matthew Henry:
A charge given to Christians to pray for all men in general, and particularly for all in authority. . . . Observe, The design of the Christian religion is to promote prayer; and the disciples of Christ must be praying people. Pray always with all prayer, Ephesians 6:18. There must be prayers for ourselves in the first place; this is implied here. We must also pray for all men, for the world of mankind in general, for particular persons who need or desire our prayers. See how far the Christian religion was from being a sect, when it taught men this diffusive charity, to pray, not only for those of their own way, but for all men. Pray for kings (1 Timothy 2:2); though the kings at this time were heathens, enemies to Christianity, and persecutors of Christians, yet they must pray for them, because it is for the public good that there should be civil government, and proper persons entrusted with the administration of it, for whom therefore we ought to pray, yea, though we ourselves suffer under them. . . .
In our prayers we are to have a generous concern for others as well as for ourselves; we are to pray for all men, and to give thanks for all men; and must not confine our prayers nor thanksgiving to our own persons or families. 3. Prayer consists of various parts, of supplications, intercessions, and thanksgivings; for we must pray for the mercies we want, as well as be thankful for mercies already received; and we are to deprecate the judgments which our own sins or the sins of others have deserved. 4. All men, yea, kings themselves, and those who are in authority, are to be prayed for.