At the New Republic, Rebecca Dana has a profile of MSNBC chief Phil Griffin, during which she points out that the network's current incarnation as the liberal's home on cable came about only because Griffin tried a bunch of other stuff that didn't work. There wasn't an ideological motivation, just a financial one. "Fox News is a TV network that succeeds because of its ideological slant," she writes. "MSNBC is a TV network that has an ideological slant because that's what happened to succeed."
That came about after a period in which the network tried hard to duplicate Fox by hiring a bunch of conservatives. At various times the network gave shows to the likes of Pat Buchanan, Michael Savage, Tucker Carlson, and Alan Keyes (the latter, called Alan Keyes Is Making Sense, for some reason didn't include "No, really!" in its title). When it turned out nobody wanted to watch any of those programs, they kept trying different things until Keith Olbermann tapped into the zeitgeist of the George W. Bush years (namely, lots of people really didn't like Bush), and they finally realized there might be money to be made in appealing to liberals.
That means that you can still have a program hosted by a conservative Republican like Morning Joe on MSNBC, because it's successful and the person running the network is happy as long as it continues making money. It also means that the network's ideological character could always be changed. That wouldn't happen overnight, because they've worked to create a brand as a liberal network (in prime time and on weekends, anyway), and they wouldn't want to undermine that brand by sticking, say, Extra Cool DeMint With Jim DeMint or Gary Bauer Wags His Finger At You between Rachel Maddow and Lawrence O'Donnell. Nevertheless, it's easy to imagine that in five or ten years, MSNBC could decide to go in a completely different direction.
Fox, on the other hand, will never change, so long as Roger Ailes runs it (and I'm guessing he'll carefully pick a successor molded in his image). Right now, of course, Fox's money-making need and its ideological need are in perfect sync, so there's little conflict between the two. But what if they started being at odds? What if Hannity and O'Reilly started to lose viewers in large numbers? My guess is that they'd be willing to try new hosts, but only those who are comfortably conservative. The network just has too much value to the GOP to ever give up.