I grew up single eye sighting.
But later in life (mid-teens) I retrained myself to keep both eyes open.
That way the sights, or scope, comes to the field of view and becomes part of the picture. Much faster target/sights acquisition.
Since I am a right handed (mainly) shooter, I usually find I have the picture as normal, and the sights or "cross hairs" seem to naturally fall into line.
For me, it was an acquired taste.
You can also wink your non-eye shut, once you are on your target.
Started out single eyed, learned to keep both open. Your brain will learn to adjust.
Not to mention breathing and heart rate into the picture.