"We, the ministers and messengers of, and concerned for, upwards of one hundred baptized congregations in England and Wales (denying Arminianism), being met together in London, from the third of the seventh month to the eleventh of the same, 1689, to consider of some things that might be for the glory of God and the good of these congregations, have thought meet (for the satisfaction of all other Christians that differ from us in the point of baptism) to recommend to their perusal Confession of Our Faith, granted for and sold by John Marshall, at the Bible in Grace-church-street, which Confession we own as containing the doctrine of our faith and practice; and do desire that the members of our churches respectively do furnish themselves therewith." (see here)
Historically, the Hardshells despise Arminianism and even those who believe it. It doesn't matter if one is only a one, two, three, four, of five point Arminian, the Hardshells do not want anything to do with Arminians. They consider Arminians to be part of Antichrist, or mystery Babylon, and will not accept them as genuine churches, or have any fellowship with them.
Though the churches who first wrote the 1689 London Confession of faith, and many churches that have since endorsed it, were deniers of Arminianism, they were not haters of Arminians. This is true today with many Calvinistic Southern Baptist churches. They tolerate those with Arminian beliefs in their fellowship and work together with Arminians to spread the Gospel of the Son of God. But, Hardshells want no cooperation with Arminians and look down on them as being inferior Christians. I think this is a terrible mistake.
It is true that there are certain doctrines that are to be "hated," such as the doctrine of the Nicolaitanes (Rev. 2: 15). But, is Armianinism such a hateful doctrine that a church cannot hold them in their fellowship? I think not.
If one reads the writings of the Hardshells, especially in the 19th century, he will see how the Hardshells used very hateful language in talking about their Baptist brothers who accepted certain Arminian beliefs, such as a general atonement. Those Hardshells despised what they called "Fullerism," the beliefs of Andrew Fuller. They even call him an "Arminian" because he believed in a general atonement, yet he was not an Arminian, for he was at least a 4 and 1/2 point Calvinist. The truth is, the Hardshells call certain doctrines "Arminian" when they are in fact not.
The English Particular Baptists who denied Arminianism nevertheless accepted the baptism of less Calvinistic churches, and have some fellowship and cooperation with them. But, Hardshells are intolerant and will not have any fellowship with anyone who is not of their Hyper Calvinistic brand of Calvinism. This is one of the things that makes them into a cult. I do not believe that their standoffishness is pleasing to the Lord. It has not been good for them as a group to have cut themselves off from other Baptists who hold to Arminian beliefs. They have missed out on the opportunity of sharpening iron, of discussing differences and commonalities, and of the good that comes from such open fellowship.
Deny Arminianism, yes. But, to refuse all interaction, cooperation, and fellowship with them, even to the point of being condescending and hateful to them, is another thing.