"They lump themselves together, in that they are both collections of non-scientists, touting theories that are not amenable to scientific methods"
On the contrary, ID disputes nothing that can be demonstrated through scientific methods.
"to the degree that they feel comfortable revising the science curriculum by force of law, over the objections of the vast majority of scientists, and the institutions that speak for scientists."
So your real objection is that they dispute the non-scientific conclusion that "it all happened entirely by accident."
ID holds that yes, it happened, but there was Intelligence behind it. The only point of dispute is the existence of God.
The same can be said for UFOlogy, and crystal healing, and pyramid energy theory. All could conceivably be true and all, like ID, lack the positive, specific forensic evidence to make scientific investigation possible.
You are correct, that is a non-scientific conclusion, so, of course, science does not draw it. Science does not have enough data to hold an opinion on this subject.
ID holds that yes, it happened, but there was Intelligence behind it. The only point of dispute is the existence of God.
Or Thor. Or Odin. Or Raynard the Dawn Fox.