FYI, butler creek makes flip up covers that are also see through. Basically the same idea as the black plastic covers except the lids have a clear inner "lens".

here's an example.
Butler Creek Blizzard Scope Cover

No problems with the covers. You flip them open as you raise the rifle. With practice it is easy to open the covers, and move to your safety in one fluid movement. Remember the safety should not come off until you see game in the sights.

Having your finger on the safety all the time (unless you are holding it in the engaged position such as when in heavy brush), and releasing it during the mount is an invitation toward disaster. The few extra nano-seconds it takes to do it safely are insignificant in the overall actions of mounting and shooting.

The see through covers introduce another set of lenses into the mix and may displace your impact point. If you use see through covers, test the impact location with them both open and closed. While rare and usually insignificant, I have seen a few times where them difference was several MOA.

Lee

Whether you choose to use the scope covers or not isn't so important as the conditions under which you are likely to need to use a scope to sight your firearm with.

If I were to plan on a lot of stalking hunting, where the chance to ambush game is likely, then I would assume that the distance at which I would engage spooked game would be minimal. In cases where I can expect spooked game to occur within 50 feet of my location at any given time, I find the use of telescopic sights rather ineffective. Usually, this type of hunting is done in heavy cover areas, although there is occasion to encounter game at close quarters in moderate cover areas.

Under these circumstances, I think that having a scope mount with a see through iron sight capability to be the best possible configuration. By having access to the iron sights of a rifle, I can instantly get on close in, moving game, and get a decent shot. Then if the conditions are such that I can set up and get on animal(s) at longer distances, I can make use of the telescopic sights and the increased magnification. Under these circumstances, the question of scope covers interfering with my hunting does not come up.

I do not recommend shooting offhand at spooked game at long distances. Most of us are not proficient enough to make a clean kill shot under such conditions. Telescopic sights are great tools, but are made for precision shooting, and do not work well for point and shoot activities. Red dot sights are another matter entirely.

I have flip-up covers on both my magnum bolt actions, and see through scope mounts on all my lever guns, which also have scope covers.

Just for the record, I have taken a shot at close-in, moving game (a spooked whitetail buck) with a high power rifle equipped only with a scope. I dropped the animal without him taking another step. I never saw the animal in my scope, and I would not ever take that shot again.