Launch Crossover
Click the Bottles button in the top-left of the window
Select the Star Trek Online bottle
Under the Gear menu pick Open C: Drive
Go into drive_c/Program Files/Cryptic Studios/Star Trek Online/Live
Duplicate the file "D3DCompiler_42.dll" in the directory
Rename the duplicate file "D3DCompiler_47.dll"
This should prevent the crash on the Cryptic loading screen - however the next loading screen will sit there for 15-30 minutes before going on to the main menu.
Looks like the update removed this DLL which was related to dropping Windows XP support but causes the game to crash in Crossover. STO may restore this DLL in a future update, but in the meantime this manual workaround should get the game running again.