R.E.D. does copies of the basic units which could be changed by certain mods, that's why you should install/activate R.E.D. after any gameplay mod.
Here's a guide that makes sure the game will load the mods in the proper order. Whenever you update a gameplay mod, I recommend to shuffle the R.E.D. mod-folder afterwards out and back into the MODS folder again while running the game, so it will load at last after activating it again. You can later check in Civilopedia if all new R.E.D. units have the same stats as the basic one. Otherwise you need to repeat the procedure until it works.
Supported mods won't work together?
Try following method while running the game:
1. Run the game and go to the Browse Mods menu
2. Install any mods
3. Alt-Tab out of the running game and filebrowse to the C:\<username>\Documents\My Games\Sid Meier's Civilization 5\MODS folder
4. Move every mod folder inside into an empty folder, e.g. \Sid Meier's Civilization 5\Patch or better into a newly created \Sid Meier's Civilization 5\Backup folder. Best to move out each mod's folder one by one, otherwise the mod list isn't always updated
5. Tab back into the game and check if the mod list in the Browse Mods menu is empty
6. Tab out and move every mod folder from \Backup back to \MODS but only one by one in the proper activation order and not all at same time!
7. Tab back into the game and activate all mods in the proper order
Here's a guide that makes sure the game will load the mods in the proper order. Whenever you update a gameplay mod, I recommend to shuffle the R.E.D. mod-folder afterwards out and back into the MODS folder again while running the game, so it will load at last after activating it again. You can later check in Civilopedia if all new R.E.D. units have the same stats as the basic one. Otherwise you need to repeat the procedure until it works.
Supported mods won't work together?
Try following method while running the game:
1. Run the game and go to the Browse Mods menu
2. Install any mods
3. Alt-Tab out of the running game and filebrowse to the C:\<username>\Documents\My Games\Sid Meier's Civilization 5\MODS folder
4. Move every mod folder inside into an empty folder, e.g. \Sid Meier's Civilization 5\Patch or better into a newly created \Sid Meier's Civilization 5\Backup folder. Best to move out each mod's folder one by one, otherwise the mod list isn't always updated
5. Tab back into the game and check if the mod list in the Browse Mods menu is empty
6. Tab out and move every mod folder from \Backup back to \MODS but only one by one in the proper activation order and not all at same time!
7. Tab back into the game and activate all mods in the proper order