I am left-handed but had to learn to wield a weapon right-handed for the SA80 and now I'm a right handed shooter!
I'm exactly the same! I am a full left-hander when it comes to almost all every-day activites. I used to shoot small-bore in a club and in Air Cadets, followed by the L98 Cadet GP also at cadets. They all demanded that you shoot right-handed because you weren't allowed to eject hot brass across your face.I still shoot my Glock left-handed though.
Later when I started competitive air-rifle shooting I tried both right and left handed rifles and couldn't get on with the left-handers at all, however when it comes to pistols and AEGs I am still 100% left-handed.
The only trouble I have nowadays is when I use optics my hands favour the right-handed rifles, but my right-eye isn't as keen as my left, something I am just working on through practice.