Try these troubleshooting steps:
Step 1) Sometimes HWR installs themselves break unexpected for no good reason. Check if your game still works properly without any mods. If it doesn't, verify the game's integrity through steam. You can do this by right clicking on the game in the library, going to properties, then local files, then verify integrity of game files. If the base game still crashes after this, uninstall it and delete all the game files and mod files, typically stored at C:\Program Files (x86)\Steam\steamapps\workshop\content\244160\ and C:\Program Files (x86)\Steam\steamapps\common\Homeworld\HomeworldRM, before reinstalling the game.
Step 2) If the base game works but the modded game doesn't, or even if the above steps didn't correct the base game's crashes, try lowering all your graphics settings to minimum. The texture size limit is probably the most important one to lower.
Step 3) If step 2 doesn't correct it and the base game works fine, steam may have downloaded a corroupted version of the mod. This happens from time to time, with all mods. Unsubscribe from the mod, then delete the local copies of the mod. These are stored by derfault in subdirectories of C:\Program Files (x86)\Steam\steamapps\workshop\content\244160\ and C:\Program Files (x86)\Steam\steamapps\common\Homeworld\HomeworldRM\DataWorkshopMODs\76561197983366846. The exact subdirectory varies from user to user, but it'll contain a Fulcrum_pub.big file along with a few others. After deleting these, resubscribe and try again.
Step 4) If none of these steps work, put "-tracehods -luatrace" (without the quotes) in the options section of the launcher, launch the game again to get it to crash, find the Steam\steamapps\common\Homeworld\HomeworldRM\Bin\Release\hwrm or hwrm.log file and post it's contents here using a service like http://pastebin.com/