The license of the IDE that was used to develop software generally does not have any impact on the licensing of the software that you wrote. The IDE is a tool, not a library. The IDE does not get distributed with your software in the end, unlike a library.
However, if you wanted to distribute a modified version of MonoDevelop, you would need to adhere to the license. In MonoDevelop's case, it is dual licensed with LGPL and MIT.
Libraries like Qt, however, do have an impact. Libraries are an integral part of your program and you need to adhere to its licensing.