Hi Pilgrim

I realize there is a lot more to hyper-Calvinism (and its various forms) than what I am about to say, but I think when someone uses the term “hyper-Calvinism” they usually mean someone who denies the free offer of the Gospel.
Those with hyper-Calvinist leanings generally speaking do not believe in evangelism.

Here is a quote from an article I found on the Highway, that I believe is quite helpful in distinguishing between a hyper-Calvinist and the historic Calvinist faith.

“In this work it has been our desire to set forth the basic theological position that all Reformed believers hold, emphasizing both the sovereignty of God aspect of salvation, and also the universal offer of the Gospel. We have tried to face some of the problems that arise out of holding both of these doctrines in tension. We have tried also to set forth what we believe to be a better form of evangelism than is so commonly held by evangelical Christians of our day. It is the prayer of this writer that this article may be helpful in guiding Christians into the most consistent type of Biblical and Reformed evangelism.”
To understand the full context of this quote I believe the whole article should be read. http://www.the-highway.com/Reformed_Evangelism.html
I also found another quote from another article, that I think is helpful.

“Conclusions
1. In persuading souls we ought to be Biblically consistent. The doctrines of grace are logical inasmuch as they are argued carefully from the Scriptures as a whole. There are, however, points that are not easily harmonised and must be left to lie side by side. We must not be supralogical and impose human rationalism where the Scriptures give no warrant for this. Arminianism and hyper-Calvinism can be charged as guilty of imposing rationalism. Both reason that ability limits obligation. 'Man,' says the hyper, 'is unable to believe and therefore cannot be required to do so.' 'Man is commanded to believe,' says the Arminian, 'and therefore he must be able to do so.' The Puritans were consistent Calvinists stressing Responsibility and Divine Sovereignty without attempting to rationalise at every point. Biblical consistency includes a clear grasp of the fact that regeneration precedes faith. We can well understand why these men knew nothing of appeals for sinners to make a recorded decision. The whole of their preaching was one protracted and powerful appeal to the whole man, that the sinner being born again might be persuaded once and for all to turn and close with Christ. If that failed other expedients could only achieve, as they so often do today, a temporary willingness to be a disciple, at the same time running the fearful risk that the person in question thinks himself saved when his heart is still in the mire. In a paper at this conference entitled Arminianisms, the assertion was made that the Bible forbids us to go one step along the road of Arminianism. That is right. It is also true that the Bible forbids us to go one step along the road of 'restrictionism'! Ought we not to exercise great caution not to proceed one inch along the road of hyper-Calvinism? This will mean that we will be on guard when we read polemical works against Arminianism. Is there not, even with John Owen's valuable polemic on Particular redemption, a tendency to neglect the urgency of the Gospel?25 It is essential that we contend for truth but in defending one aspect it is possible to neglect another of equal importance. The quotation with which we began is in no way inconsistent with the careful exegesis of Owen's above mentioned treatise.” http://www.the-highway.com/Puritans_Hulse.html
All that said I have no idea whether this is the aspect that seems to get some Arminians of Dutch descent dander up. Perhaps I will never know seeing that it would be a very unpleasant and unfruitful conversation if I brought the topic up with them.
Perhaps hyper-Calvinism isn’t the real problem; it might be something like the Calvinist doctrine Limited Atonement that upsets them?

Tom