Right click on the *selected* Text in the Inspector and select in the popup menu, select Substitutions > Replace Quotes:
For a complete explanation of how this feature works... you'll have to look it up. I think the "checked" settings only "stick" on a Title by Title (or text object by text object basis) unless you change global system settings in Keyboard > Text Preferences.) That said, Replace Quotes may only work if the settings are set up in Keyboard Preferences...
I do know that you can apply a Title, right click in the Text inspector, Set Smart Quotes, and all the straight quotes you use from that point on will automatically change. You can go back and unselect Smart Quotes, the curly quotes already applied will remain, but further typing will maintain any straight quotes you use from that point on.
This feature works on ALL selectable text in FCPX, including Renaming Clips.