Whatever works for you is what's right for you.
That being said, here's some thought process to consider. I used to be a photojournalist and spent a long time training myself to shoot with both eyes open. This is important because as a journalist, you shoot what's happening as it happens. There is no restaging of a sequence. When shooting sports, especially basketball, soccer and football, you need to keep an eye on where the ball is as well as players that are close to you to get the best shot and avoid injury.
You can shoot with both eyes open using either eye but since shutter releases are always on the right side, your right-hand will significantly block your peripheral vision.
So, while what you shoot now may not require maximum viewing area, it's worth keeping in mind.