I have a project (code) that I am wanting to license as MIT. It has a few dependencies, mostly assets (icons and images). Some dependencies are MIT and I include their licenses in the source, but a few are CC BY-SA. If they are ShareAlike, does that mean my project that uses them has to be CC BY-SA as well? Do I have to give up the MIT license?
CC-BY-SA 4.0 requires that
if You Share Adapted Material You produce, the following conditions also apply ... the Adapter’s License You apply must be a Creative Commons license with the same License Elements, this version or later, or a BY-SA Compatible License.
and says that
Adapted Material means material subject to Copyright and Similar Rights that is derived from or based upon the Licensed Material and in which the Licensed Material is translated, altered, arranged, transformed, or otherwise modified in a manner requiring permission under the Copyright and Similar Rights held by the Licensor.
IANAL/IANYL, but as I read it, this says that anything that copyright law regards as a derivative must also be licensed under CC-BY-SA (or a compatible licence, which the MIT licence is not).
What constitutes a derivative work is a contested issue, but one broadly-supported approach is that things that share complex, custom structure are parts of the same work. So any of your code that links into the CC-BY-SA assets, or anything that uses its internal formats, is arguably part of the CC-BY-SA work, and will need to be CC-BY-SA also.
All the rest of your contributions can likely be under MIT, or any other licence that you choose.
You don't tell us what the CC-BY-SA assets in question are, or how you are using them, so it is difficult to be more precise than this.