If Material Design Icons is even based on Font Awesome, and if the code points and font weights of the characters are the same, then one possibility is that it is missing a number of characters that Font Awesome has. When comparing the file sizes of Material Design's font files with that of Font Awesome, Material Design seems to take up significantly less space overall.
Material Design has a version number like 5.5. However, XenForo 2.2's Font Awesome has a version number like 5.14. If they are both based on Font Awesome, the result would be a number of missing characters.
If Material Design is based on Font Awesome and is not missing characters, but even the font weights are different than default XenForo, then Material Design will not work with VaultWiki...
If you change the font weights of the characters used by VaultWiki in such a way that a different FA-style is being used than the one VaultWiki intended, or if a different character is now being used that is not part of Font Awesome Free, then you will be violating Font Awesome's license terms, unless you purchase a Font Awesome Pro license specifically for your site. Even if you have a Font Awesome Pro license for your site, if affected icons are available in the wiki's icon font chooser, and more than just you has access to the chooser, then you would still be violating the Pro license's terms. This is based on prior consultation with Font Awesome's team about VaultWiki's usage of icons. VaultWiki's icons were carefully chosen from the files that shipped with XenForo based on the results of these talks.