I think now would be a good time to remind readers (and myself as well), that the Flat Earth issue is only a small sliver of the Conflict Thesis issue, and besides has its own thread currently on this forum.
As @TedDavis reminded us, there have been a number of conflict-related views, both historic and modern. Wikipedia sites the Conflict Thesis in a wider framework of an ‘Incompatibility’ perspective. And I cannot help but wonder if this isn’t a better general label – the viewpoint that science and religion do things differently. This need not necessitate conflict – a ‘live and let live’ might prevail. But it can also, at times, lead to a ‘my way or the highway’ attitude.
On the latter point, I am still unwilling to accede to Kemp’s ‘both sides are to blame’ framing of this. I have yet to see even the most strident atheist advocate for forcing evolution into churches, let alone write legislation attempting to make this law. I have however seen no end of (both proposed and in a few instances passed) religiously-motivated legislation that attempts to control what is taught in Public School (and thus, by the Establishment Clause, secular) science classes.