I'm right handed but shoot left handed, for me though its not because I have one eye dominant over the other, its purely for comfort and feel.
It just feels more natural to me for some strange reason.
My rifles are all left hand bar the Tikka T3x Ace game that I bought at the end of last year.
I had to get a r/h 6.5prc and it wasn't available in left hand.
The chassis is obviously ambidextrous, but operating a right hand safety catch is a bloody pain in the arse when you're shooting left handed.
I actually wish I had just held off for a while until the Left handed ones become available, or just sourced a chassis and had one built