I was thinking about creating an application for the Mac App Store, but was wondering if they will only accept programs made in Objective-C using XCode.
I was thinking about making the program multi-platform by using Qt, so I can release Windows and Mac versions.
Considering that I don't represent Apple, and haven't seen any examples where this debate has played out yet in favor of one side or the other, it's difficult to give you a definitive answer to this question. Instead, I'll post what look like the relevant sections of the Mac App Store Review Guidelines and let you decide for yourself.
First up is Section 2 on "Functionality". This a pretty broad topic area, and it appears to me that there's lots of potential for violations using a third-party GUI library. Of course, I also think all of these can be worked around, if you're sufficiently interested.
2.5 Apps that use non-public APIs will be rejected
. . .
2.14 Apps must be packaged and submitted using Apple's packaging technologies included in Xcode - no third party installers allowed
2.15 Apps must be self-contained, single application installation bundles, and cannot install code or resources in shared locations
2.16 Apps that download or install additional code or resources to add functionality or change their primary purpose will be rejected
. . .
2.24 Apps that use deprecated or optionally installed technologies (e.g., Java, Rosetta) will be rejected.
. . .
2.29 Apps that do not use the appropriate Mac OS X APIs for modifying user data stored by other apps (e.g bookmarks, Address Book or Calendar entries) will be rejected
Section 6 on the "User Interface" is also worth considering for an application that uses Qt. I refuse to use the library on Windows because it doesn't use standard platform GUI elements. I can only assume it does the same thing on the Mac, and it remains to be seen how Apple will react to that. (I suspect alternative cross-platform GUI libraries that behave correctly and use native widgets are free and clear here.)
6.1 Apps must comply with all terms and conditions explained in the Apple Macintosh Human Interface Guidelines
. . .
6.3 Apps that do not use system provided items, such as buttons and icons, correctly and as described in the Apple Macintosh Human Interface Guidelines will be rejected
. . .
6.5 Apps that change the native user interface elements or behaviors of Mac OS X will be rejected