Thank you for adding your insights and nuances to this post, James. I fully agree with this part of your comment--which is a central point in a book I'm finishing--and much of the rest. I hope you will come back often to my blog and contribute. Let me simply say, for the benefit of other readers, that James is finishing a doctorate in history of science under Peter Harrison at Queensland--which is a very high qualification.
I didn't know some of this information, though I can't speak for Steve Snobelen. I know much more about White than about Draper. I know their two big books quite well, especially White's (even bigger one), with which I've been working fairly extensively recently as I complete a project about American religion and science in the early 20th century. And I have a decent working grasp of White's career and other work--but not Draper. If we limit the field to Draper's book on the conflict thesis (leaving out his earlier book on the intellectual development of Europe, which I have not studied carefully though I have a copy), I think it's fair to say that Roman Catholicism was his major target. Protestants are given a pass, but Muslims and Protestants come off better than Catholics. Draper simply hated Catholicism partly for family reasons; on this, listen to Ron Numbers' podcast here: http://www.hup.harvard.edu/news/audio/9780674057418-HUP-Podcast-Ronald-Numbers-on-Galileo-Goes-to-Jail-and-Other-Myths-about-Science-and-Religion.mp3. In his view (as seen in the book), the Catholic Church was so closely tied to political power that they merited a special animus. Ultimately (consistent with what you say) it was ecclesiastical power that he detested, and Catholicism just had more of it.
A lot of work remains to be done on both men and their legacy. I was part of a conference on this two years ago http://www.issacharfund.org/madison-may-2015 and learned much from it, but I don't recall learning very much about Draper's background and don't recall anything about any specific attacks on fellow Protestants such as those you mention. Again--thank you for this.
As for White, we agree that White made a wholesale attack on Christianity, but it was specifically Christian thought that he attacked wholesale, not Christian ethics, which he wanted badly to preserve. In his view, Christian thought and Christian higher education were essentially oxymorons--a view that seems to be shared by Dawkins, Coyne, and Sagan among others. He wanted a purely secular education; indeed nothing else in his view was worthy of being called education. Incidentally, White's college roommate at Yale was none other than Daniel Coit Gilman, the first president of the first research university in the USA, Johns Hopkins. I don't think it's an accident that the public launching of JHU included an address by Thomas Henry Huxley, who also had a very low view of Christian education.
Perhaps the best indication of White's agenda is the flowery preface to his magnum opus: http://www.gutenberg.org/files/505/505-h/505-h.htm, especially the final lines: "My conviction is that Science, though it has evidently conquered Dogmatic Theology based on biblical texts and ancient modes of thought, will go hand in hand with Religion; and that, although theological control will continue to diminish, Religion, as seen in the recognition of "a Power in the universe, not ourselves, which makes for righteousness," and in the love of God and of our neighbor, will steadily grow stronger and stronger, not only in the American institutions of learning but in the world at large. Thus may the declaration of Micah as to the requirements of Jehovah, the definition by St. James of "pure religion and undefiled," and, above all, the precepts and ideals of the blessed Founder of Christianity himself, be brought to bear more and more effectively on mankind."
Anytime you encounter language of that sort in an early 20th century American author--especially the reference to "pure religion and undefiled"--it's likely that you're seeing White's footsteps. He did indeed want a type of liberal religion that jettisoned the bodily Resurrection and the Deity of Jesus while keeping the Sermon on the Mount. As the later "modernist" Christians would say, they wanted the religion of Jesus, not the Jesus of religion.