Not coincidental, they both stem from the directional description "right".

In Old English riht meant both straight and not left. That's why "go right ahead" and "go straight ahead" are synonymous even tho that sense has been largely lost.

"Right" then got the sense of proper/correct, likely because right-handedness is more common and thus the right hand was associated with being the "correct" hand. This is why you are "dextrous", from Latin dexter meaning directionally right.

The political "right" as in conservative also comes from the direction right because in the French National Assembly after the 1789 revolution, the conservatives sat on the right while the progressives were seated on the left.