The two men were J.S. Mill and H.G. Wells.
Mill thought it possible to hold in conjunction a belief in a "religion of humanity" with a belief in Manichaeism - a gnostic religion centred in Persia which thrived for several hundred years (3rd - 7th centuries A.D.)
Wells's religious beliefs have been described in detail in an impressive article by Willis B. Glover. Like Mill, Wells rejected Christianity:
Wells ... reacted violently, even as a child, against the evangelical faith of his mother. This hostility continued throughout his life and included both Protestant and Catholic Christianity. (p.121).
Wells was so opposed to Christianity that he envisaged strict methods to circumscribe it in his future utopia:
Wells does not hesitate to picture an ideal society of the future in which the propagation of the Christian faith, if persisted in, would be punishable by death; and he justifies this by analogy with legal requirements for vaccination. (pp.123-124)
In 1917, Wells advanced his ideas for a "modern religion" in his work God the Invisible King:
The content of the religion which Wells heralded with such confidence and enthusiasm is an amazing concoction of humanism, Christianity, Gnosticism and a kind of Promethean dualism to which Wells later called particular attention as giving him affinity with the Manichaeans. (p.125)
There is a lengthy description of the theology of this religion on pages 125 to 128. It includes an opposition between a "Veiled Being," who is the author of nature, and a finite God whom we are to worship:
Wells begins by distinguishing the God of his faith from the "Veiled Being" who is behind and in some sense responsible for the universe in which man finds himself ... the Nature for which this being must be held responsible is the real enemy of man, the source of his suffering and the obstacle in the way of his progress.
The God of H.G. Wells was a finite God who had a beginning in time but who was outside space. God was a person who was the Captain of Mankind ... God had come into existence "somewhere in the dawning of mankind" and "as mankind grows he grows".
With our eyes he looks out upon the universe he invades; with our hands he lays hands upon it ... He is the undying human memory, the increasing human will.
The enemy ... was Nature ... God stands over against not merely the ultimate being who is referred to as Darkness or the Veiled Being, but also against the Life Force, which is a lesser being coming out of the Veiled Being ...
... for the present God and mankind are in a state of opposition to the universe and to the Life Force within it. God is described as an unfilial, Promethean rebel ...
Wells frankly accepted the dualistic character of his religion and even after the failure to launch a new religion of mankind he referred to his own religious outlook as Promethean, Manichaean, and Persian.
As Glover notes, the new religion didn't take off and Wells retreated from pushing a theology.
What would this kind of religious gnosticism have contributed to? Possibly to a radical rejection of the world we live in as being false, dark and oppressive, a creation of the Veiled Being and the Life Force, from which we seek to escape as a species as the agents or co-workers of a divine purpose.
If this is your religious view, then it makes sense to be hostile to tradition, to look for a revolutionary change in the conditions of life (a transfiguration of reality) and to want a central world government to direct human affairs.
You get a sense of this in an article about Wells by Fred Siegel titled The Godfather of American Liberalism. Wells appears to have had a significant influence on American (and Anglosphere) thought:
By 1920, The Nation could describe Wells as “the most influential writer in English of our day.” ... For many, noted historian Henry May, Wells was “the most important social prophet.” The social critic Randolph Bourne described Wells’s “religious” impact, his “power of seeming to express for us the ideas and dilemmas which we feel spring out of our modernity”—a power that was nothing less than “magical.”
Orwell nonetheless recognized Wells’s extraordinary impact. “I doubt whether anyone who was writing books between 1900 and 1920, at any rate in the English language, influenced the young so much,” Orwell wrote. “The minds of all of us . . . would be perceptibly different if Wells had never existed.”
“Without doubt,” wrote Brooks, “Wells has altered the air we breathe and made a conscious fact in many minds the excellence that resides in certain kinds of men and modes of living and odiousness that resides in others.”
Other major public figures in the U.S. acknowledged Wells’s impact. Margaret Sanger ... believed that the author had “influenced the American intelligentsia more than any other one man.” The naturalist Joseph Wood Krutch, looking back on the 1920s, noted of Wells that “a whole surviving generation might appropriately sing in the words of the popular ballad of their days, ‘You made me what I am today.’ ” To assess Wells and George Bernard Shaw, Krutch asserted, “would come pretty close to assessing the aims, the ideals, the thinking and one might almost say, the wisdom and folly of a half-century.”
Wells's influence was for transformative change. Literary critic Floyd Dell wrote:
Suddenly there came into our minds the magnificent and well-nigh incredible conception of Change. . . . gigantic, miraculous change, an overwhelming of the old in ruin and an emergence of the new. Into our eternal and changeless world came H. G. Wells prophesying its ending, and the Kingdom of Heaven come upon earth; the heavens shall be rolled up like a scroll, and all the familiar things of earth pass away utterly—so he seemed to cry out to our astounded ears.
Wells himself placed great hope in Theodore Roosevelt as an agent of change:
“My hero in the confused drama of human life,” Wells wrote in The Future in America, “is intelligence; intelligence inspired by constructive passion. There is a demi-god imprisoned in mankind.” ... Wells presented TR as the demigod incarnate, the very symbol of “the creative will in man.” Here was the man of the future—“traditions,” noted Wells, “have no hold on him” ... “I know of no other,” said Wells, “a tithe so representative of the creative purpose ...
There's not much room in this for a sympathetic defence of tradition in general, let alone particular national traditions. It's all to be cast off to liberate the "creative will" or the "creative purpose" in man.
Wells is an example of an influential thinker within the liberal tradition, whose gnostic and humanistic beliefs set him radically at odds with real, existing, particular traditions.