The only files I see that they have in common are the commands_xx.cfg files and cameras.dat. Other than that, FMNI doesn't seem to overwrite anything that Conus's mod also changes.
I don't know what controls the gunsights so I'm unsure if the files noted above would be what is causing the problem. I'd really like to know where the issue is too, as I have them both in my mods list, but I'm still testing out my combo for other things and I don't think I've done any shooting or targeting... mostly just making sure the game still loads and the boats themselves look good inside and out.
Edit: altho I should say, if you are going to enable FMNI over Conus's WS mod, you should follow the instructions included in documentation for the former regarding making the necessary changes to the commands_xx.cfg files manually instead of just letting the files get overwritten in JSGME. I can't remember if Conus's mod contains any changes to them other than phrasing of certain messages you get from the crew, but it's been a while since I looked at them and I always edit those files manually for compatibility since so many of my mods make changes to them. They're not files that you want to just overwrite any time a mod gives you different versions of them, because you risk losing stuff that is necessary for the proper functioning of another mod that was previously enabled.
I'd have to look at the cameras.dat to even see what the differences are there.
Edit2: Looking at cameras.dat, just at the node for UZO under CameraParams for the Viewport the settings for Left and Right are different in FMNI than in Conus's mod. The ones in FMNI match what I see in the file from an unmodded GWX installation, so Conus changed something there that was necessary for the new WS layout. If you enable FMNI over top of the WS mod, you get a new file that includes stuff FM did for his mod, but you're losing some of the changes to it that Conus did for the WS layout. What you need is a new cameras.dat that works for both mods (in addition to making sure the commands files are compatible with both as already noted above. I don't know if that will solve the problem, but I have a gut feeling that it might.