Is It Illegal to Teach Intelligent Design Creationism in American Universities?

Jerry Coyne has discovered that a course at Ball State University (Indiana) teaches science from a viewpoint that's sympathetic to Intelligent Design Creationism [“Science” course at Ball State University sneaks in religion]. It looks like a really bad course and I'm glad that it's getting a lot of negative publicity. It looks like the instructor is advocating Intelligent Design Creationism.

I defend the right of a tenured professor to teach whatever he/she believes to be true no matter how stupid it seems to the rest of us.¹ I'm troubled by the fact that some people are calling for the instructor's dismissal and writing letters to the chair of his department. We really don't want to go down that path, do we? Academic freedom is important and it's especially important to defend it when a professor is pushing a view that we disagree with.

But that's not the only troubling thing about Jerry Coyne's post and the comments it has stimulated. Jerry thinks that it is unconstitutional (i.e. illegal) for a university professor to be advocating religion in a publicly-funded university. He says,

Ball State University, in Muncie, Indiana, is a public university (i.e., part of the state university system). As such, it must abide by the First Amendment to the U.S. Constitution, which has been interpreted as disallowing religious viewpoints (or religiously based theories) in public-school science classes. It is of course kosher to teach courses on the history of religion, or on the relationship between science and religion, but those must not pretend to be “science” courses, and must present balanced views—they can’t push a particular religious viewpoint.

But it’s come to my attention that a science course at Ball State University—actually two courses, because it seems to be cross-listed—is little more than a course in accommodationism and Christian religion, with very little science. It’s my firm opinion that teaching this course at a state university not only violates the First Amendment, but cheats the students by subjecting them to religious proselytizing when they’re trying to learn science.

Is he right? Does the US Constitution really specify that you can't advocate a religious viewpoint in a university classroom?

That's very scary. It probably means that you can't criticize religion either. Does this mean that there's going to be a bevy of lawyers on both sides of the issue examining the content of university courses all across America?

UPDATE:
PZ Myers: I have to disagree with Jerry Coyne

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1. There are some limitations, but let's not quibble over details. Teaching that Michael Behe, Ken Miller, Francis Collins, and Bill Dembski might be right don't qualify as exceptions.