I can't release MIT licensed code that links against a GPL'd library. That's a pretty huge incompatibility if you ask me.
Of course you can. The belief that the GPL is "viral" or can somehow infect unrelated software is spread by groups opposed to widespread creation of GPL'd software.The GPL is a copyright license. It applies only to cases covered under copyright, eg, distribution of the original and derived works. This means you can release code under any license that links to GPL'd code. If you create a derived work (eg, compiled binary) from both original works, you'd need to abide by the terms of both licenses.
For example, say you have an application under the MIT license, and you'd like to support a GPL'd library. The resulting license tree would look like this:
MIT (app code) GPL (library code)
| |
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GPL (app binary)