Fred Bear, an iconic figure in modern traditional archery - threw right-handed, and shot firearms with his right - but he wrote with his left, and shot a left-hand bow throughout his life, even after he went to a compound bow.
My son, throws, writes, eats right handed. He shoots a rifle and bow, left handed.
I do the same, long arms and baseball bat right handed. Handgun and bow left handed. I’m a southpaw, my Dad was right handed. Dad taught me to shoot shotgun, rifle and howto bat. Taught myself the bow and handgun😊
IIRC, GarandThumb on YT is left handed and shoots righthanded.