I am wondering if one mounts a scope, is it better to align the crosshairs with the action as in using two levels in ways described in one of the popularly sold scope mounting tool kits,
or
it it better to align to the center of the earth when long gun is mounted to one's shoulder in a possibly slightly but repeatable canted position, essentially eyeballing it to take into account a less than perfect shoulder mounting and holding for a shot?

Sorry, there may be better ways to set up this question and the issues involved. Maybe someone can state the question or issues better.

I just do it by eye. Throw it up quite a few times and ask yourself "IF" it could go one way to better level it, which way would it be? When you can't decide which way would be better, it's done.

Mount the scope square with the rifle, and mount the rifle plumb with the earth. A scope level is a handy teaching tool to build the correct muscle memory when mounting the rifle.

I know that I personally cant the rifle slightly when shooting offhand, but don't cant when shooting sitting off sticks.

So, I would always mount plumb with the earth. I can adjust from there if needed by changing form. But once you have mounted the scope with your preferred cant, it is then off-kilter for any other scenario.

This seems to me like mounting the steering wheel on my truck crooked to compensate for a bad wheel alignment. I would prefer to mount my steering wheel parallel with the tires, and get a wheel alignment done...

That's actually what I was trying to say. Just mount everything straight and then force your body to adapt correctly from there.

A trick I use, and actually came up with on my own, is to aim at my refection in a mirror. If the vertical cross hair bisects the muzzle, then the reticle is lined up to suit me. I doesn't matter if the rifle is canted, or hell, even held sideways. If the cross hair bisects the muzzle, you are good to go. Of course this assumes a scope mounted over the bore, not offset for some reason. And you still have to not cant the rifle on extreme long range shots.

This is the correct answer, always mount the scope square with the rifle. If you're canting the rifle then you need to adjust your form, not mess up the scope/rifle setup.

This is purty much what I do.

Ah, my mistake. I misunderstood what you were saying.

It's not as critical how you mount the scope for shooting offhand, but once the distances are stretched out past 300 yards, you need to be sure those crosshairs are level to the world. Then you should also be worrying about a scope reticle anti cant device such as a scope level. This is also very subjective, as some shooters are better than others at naturally holding their rifles level while shooting. For some, an anti cant device isn't necessary until shots are taken well over 600 yards. What also isnt discussed is rifle fit and each shooter is different. Ill give a good example: most rifle manufactures cater to the right handed shooter. If you shoot left handed with a right handed rifle, the natural fit of the stock to the shooter, may actually leave the rifle slightly canted. I for damn sure am not going to throw up my rifle and have to adjust the rifle before a shot every time. Thats just not natural and it takes from the speed and agility of getting on a game animal. For this reason, I'm in agreement with the others about adjusting the crosshairs for your own personal fit. Remember, they need to be level with the world not necessarily the action of the rifle. However, at extreme ranges that most of us will never shoot a game animal, there will be a slight discrepancy in poi because of the axis of the reticle isnt perfectly lined up with the vertical axis of the bore. Where's mathman at. He may be able to trig that error out. That also depends on how far out that alignment is. Likely in a real world situation, you wouldnt notice enough of a difference until way past 800 yards. If we were shooting a mile, my answer would be different.

Assuming the scope is mounted 2" above the bore, and a cant between the reticle and the bore of only 5 degrees, this results in a 0.16 MOA windage offset. A cant of 10 degrees is 0.33 MOA offset, etc.

Nobody is suggesting you adjust the rifle before every shot, but I'm suggesting the OP uses a scope level to practice correctly mounting the rifle to his shoulder to develop the muscle memory of mounting the rifle level each time. Then by mounting the reticle square to the receiver, he'll have developed the muscle memory so that the rifle and the scope are square and plumb with the earth, without having to think about it or adjust each time he shoots.

I’m really not that sophisticated as I’ve never even thought about some of those things. I just mount the scope and try to make everything look right.

Thanks to all who responded.
Lots of ideas to think about.

Uhhhh....

Level the action then level the scope.

Best of both worlds.

As Jordan Smith said, “Level the scope so it’s square to the action”(directly above the center of the bore....with no cant). It doesn’t take much to develop the correct muscle memory so that when you bring the rifle to your shoulder it is square and the reticle looks straight. Usually just shouldering the rifle a few times is all it takes and your body begins s to compensate.

Leftybolt

I leveled mine to the eye until I bought a scope mounting kit. Every scope on every rifle was crooked as hell. Once I mounted them all level with the action it made it much easier to sight in. The bullets on paper went straight up or down when I adjusted elevation, level across the paper, when I adjusted windage. It explained the difficulty I’ve had sighting in at times.