I'll tell you this: I've been involved with fonts on Macintosh since before there were "outline fonts" (since System 1.2). Fonts have been one of the greatest strengths and selling points for Macs and at the same time, one of its greatest weaknesses (a corrupt font can cause all kinds of havoc - duplicate fonts cause problems, etc.). My point being, I have a lot of experience with fonts and I still can't tell you what your specific problem will be.
The font you're referring to is Stone Sans ITC TT (or one of its five variants). There is a 99.9% probability that you obtained it when you installed FCP Studio (or iWork). The fact that it is installed in your user account is surprising. On my system, it's installed in /Library/Fonts (globally accessible).
Try this: find the fonts in ~/Library/Fonts (your user account library) and move them out to another location, then (restart Font Book if it was open and) install them into the Computer fonts in Font Book:

Drag the font directly into the font list column.
[*uninstall from within Font Book? You'd have to dig it out of the Trash... I personally prefer not to do that.]
The change in location won't make a difference to Motion and they should always be available regardless of which user account you may be using at the time (or which application you are using).
If you find you have duplicate fonts? Remove (or deactivate) the font from the User account. You are not supposed to have two copies active at the same time. [This is another mystery that stymies me: there are approximately 4 dozen fonts installed for FCPX **in** FCPX, the same fonts are installed inside Motion. If you want to use them in other applications, you have to copy them out of one or the other app and install them for system-wide use in Font Book giving up to 3 duplicates of a single font — but this doesn't cause OSX a problem! But 2 duplicate fonts at the user/computer level wreaks havoc. 😝 ]
Are the Share errors just since FCPX 10.3?