The NY Times has an article about the puzzling lack of conservative playwrights. The lack of “fair and balanced” political perspectives in regional theaters and festivals is pretty clear, but the fact that interviewees couldn’t think of any contemporary conservative playwrights is a bit odd. I would argue that Neil LaBute is a little right of center — he addresses cultural politics and doesn’t construct paeans to Iraq war, though. I am thinking particularly of The Shape of Things.
I think a far bigger factor is the kind of resurgence and celebration of anti-intellectual and anti-“elitist” sentiment in the broader conservative movement. Going to see a play is definitely elitist, and the kind of Bill Buckley conservatives who would write theater are a bit rarer in the younger generation of playwrights. I’m surprised that some libertarian or objectivist playwright hasn’t popped up, but after reading Ayn Rand’s attempts at theater, it is tempting to think that the ideology doesn’t make for riveting drama.
An Ergodic Walk 
I think part of the problem is that art often requires challenging convention, and despite trying to portray themselves as the “mavericks,” conservatives are generally the party of the establishment. A conservative would have written a play where Willy is a great success and Biff is an obedient and dutiful son, but would that have been nearly as interesting? Drama that upholds convention is arguably propaganda, but almost certainly boring.
I guess that you see more conservative writers or directors in film. David Zucker of Airplane, Naked Gun, and now the truly unfunny AN American Carol comes to mind.
Leads to another question… what are some examples of funny conservative humor?
(South Park doesn’t count, even though, 4 years ago, the GOP tried to claim that this show played on their team)
The conservative viewpoint (that our social institutions may have evolved by accident, but that this makes them better, not worse, than the alternatives offered by progressives) is respectable, sometimes correct, even, but not especially amenable to putting on the stage. Gilbert & Sullivan did it with Patience and HMS Pinafore. Hard to top that performance, I’d say.
Now if you mean conservatism as merely the current politics of the right wing, well, just where can a conservative playwright find enough actors willing to audition? Demography is destiny..
I’d say that conservatism isn’t so much anti-intellectual as that “intellectuals” (academics, playwrights, Manhattanites and San Franciscans) are anti-conservative. (It’s hard to reconcile conservatives being anti-intellectual with their post-Reagan hero being Hoover Institute Fellow and author Newt Gingrich.) I think that explains that lack of a point of view: If you knew that your political views could damage your career, would you let them be known? Would you even stay on a career path where your political coworkers assume that their peers are fellow liberals and that conservatives are neanderthals? If you knew of no audience for your politics, would you risk your livelihood on inventing one?
To answer one of the aforementioned commenters, funny conservative humor does exist. South Park does count – although not all of its political humor is conservative, its conservative satire is as humorous as the satire on it which isn’t conservative in nature. Then there’s PJ O’Rourke. Frank’s posts at the decidedly conservative humor website imao.us are funnier than any liberal counterparts I’ve seen (especially the satires of Frank’s “In My World” series). And I, for one, am partial to the now-defunct Allahpundit website; the anonymous author now writes “straight” for Malkin’s Hot Air, but many of his posts are humorous in nature. Oh, and he’s a New Yorker; imagine that, a conservative New York writer having to keep his anonymity.
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An alternative theory on the “anti-intellectual sentiment” within conservatism is as follows: Intellectuals propose change for society, whether for good or ill. Conservatism is defined as resistance to change, good or ill. Therefore, conservatism and intellectualism are inherently at odds. If you think the proposed changes would be bad, the intellectuals would seem more dangerous. If you think the status quo would be bad, the conservatives would seem more dangerous. It’s a bit reductionist, but it explains this in broad strokes.