"There is a resurgence of religious people who want to present to the public that science supports their specific religion."
That's true (of Buddhism, Hinduism and various cults as well as Christianity), but that's not what Intelligent Design is. It is a very broad movement (if it can even be called a Movement). It is not necessarily even Theist per se, as you point out, though of course in practical terms most of its proponents will be Theists. But it says nothing of the nature of the Intelligence behind the Design, and is not intrinisically religious but a valid scientific line of enquiry.
"We allow religionists to influence scientific discussion without challenging them on it"
Seems to me that "Science-ists" (as opposed to Scientists) think that the reverse is okay - it's fine for "Science" to influence religion, but not the other way round.
It also assumes that materialism is the only valid philosophical basis for science, which is not a rational assumption and in fact ignores the history of science in the real world, and the place that Theism has played in it, from Christian, Jewish and Muslim scientists over the past thousand years or so.
As for ID, it is argued for by its proponents on at least as rational and scientific a basis as those who argue for non-Intelligent Design (or is that non-Intelligent non-Design?). The arguments from "Irreducible Complexity" for example, are logically powerful and not ones that can be summarily dismissed and pooh-poohed just by taking an a priori materialist stance. They are not a priori but a posteriori arguments based on deductions from observation of physical reality and must be answered as such with logical counter argument and evidence. So far I see little of that in the response of the Dawkins brigade, but simply a smug, demeaning "oh this is not real science" and "we know better than you," attitude. They are the Spanish Inquisition of the Scientific World, not interested in Truth but mere Conformity.
