Tbf, if they didn't show him writing with his right hand, this would all be acceptable.
I write with my left hand, but play guitar right handed, pitch a baseball right handed, do basically everything right handed, except usung my left to write and do knife work in the kitchen.
Left handed folks are often ambidextrous.
Not to mention he's religious and back a number of years, you weren't allowed to be left handed, so maybe that is why he writes with his right hand in the scene, and maybe why it's such a liberation for him to come out as left handed? Idk