For most people an object 100 yards away is "distant enough." If you're unable to pick a thumb (one is clearer than the other) when focusing that far away, it's likely that neither eye is sufficiently dominant for your brain to have learned to ignore the other image - or that your distant vision is poor enough that you're not really focusing on the far object* - just "blindly pointing at it".(?)
When you focus farther away, everything up close is seen in "double vision," and if your brain doesn't "filter it" to remove one or the other of the two pictures confusion is likely.
(Perhaps we should suggest that nobody should offer "that explains a lot about topsie" but I'm not gonna say anything.)
The same thing happens when you focus on something up close. Everything farther away is seen in double vision, but most people adapt so as to ignore (or just "blur out") the parts of their field of view where the parallax effect is too significant for comfort.
If your eyes are so well matched that neither eye shows easily observable dominance, it shouldn't really cause any significant problem as long as you're aware that you may need to close one eye for some tasks that require "critical focus."
For the above cited pistol shooting, it is absolutely essential that your point of focus must be on the two sights, front and rear, of the pistol. Those two sights must be aligned with each other within about 0.001 inches or less to hit the center ring on the target. There's no problem at all if the target is nothing but a blur, because even a blur has a center and that's what you're trying to hit.
A situation you're perhaps more likely to encounter, where suppressing (closing) one eye may aid in getting the sharpest possible focus with the other eye might be something like threading the needle on your sewing machine. With one eye shut, you lose the aid of any "stereo depth perception" but may gain enough from seeing a single image more clearly so that you can hit the hole in the needle more accurately. (For hand stitching, you don't put the thread through the hole in the needle. You hold the thread up and put the needle on it - as I'm sure you've been taught. A much easier task.)
* As people age and their "depth of field" diminishes, it's common to prescribe lenses that actually set the maximum distance to which you can focus at about 2/3 of the way to the farthest thing you might need to see with some clarity, to take advantage of what's called the "hyperfocal point." Focused at 2/3 of the way (approximately) to the farthest point that's significant gives a camera the maximum possible depth of field, so that the largest part of what's beyond the focus, and the largest portion of what's in front of it, are "least blurred." While this (sort of) works for people, in most cases the camera only has one eye while we (mostly) have two, so "brain power" is still necessary to help us "ignore what doesn't fit."
(Maybe you're experiencing a deficit in your "ability to be sufficiently ignorant"?)