Potter on Being an "Old Baptist"

Elder Lemuel Potter, in writing of the English Particular Baptists who wrote the 1689 London Confession, wrote the following:

"In our efforts to identify ourselves with the Old Baptists, against the claims of the missionaries, we claim to be identical with these old English brethren in doctrine. THE ADVOCATE does now stand, and always has stood there, especially on the new birth. We hope that none of our brethren will differ from them, and at the same time claim identity with them." (See my citation in full here)

I agree with Elder Potter that those who call themselves "Old Baptists" and yet disagree with the London Confession, are inconsistent and contradictory.  What say ye, my Hardshell brethren?