It seems like the current standard is with the body straight and parallel to the barrel so the recoil is not at an angle. I don't buy that reason because all the rifle cares about being square is the 2 inches of shoulder it's touching and that is not necessarily square to the body position.
Do you think in-line is superior to angled?
Related question: tilt neck back and look 'forward' or leave face down and look sharply 'upward' with the eyes?
I was glad to see this question as I think it’s good to have more threads about technique. This will be a long response, but the OP raises good questions and I hope I can help by describing my learning curve.
Sometimes I shoot with sling and jacket, sometimes FTR, and sometimes F-Open, though even in F-Open I shoot with a bipod. My first F-Class shooting was FTR, and when I started I’d already been shooting smallbore prone with sling and jacket for a while. So, when I started FTR I figured I’d duplicate my sling position: Body at an angle to the rifle, left leg straight back (I shoot right-handed), right leg curled forward, body tilted left to get my chest off the ground and breathe easier, rifle’s butt sandwiched firmly in my shoulder pocket.
I quickly learned it didn’t work for FTR. In F-Class, my left forearm is resting on the mat, and my left hand is curled around the front of the rear bag, squeezing it to make minor aiming adjustments. The tilting posture from smallbore prone was too uncomfortable, at least for me.
Then I went to the position I see many F shooters use: torso flat on the mat, body directly behind the rifle. Many people shoot well that way. When I did it, it was uncomfortable, I had more trouble breathing, and the gun torqued so much I had to significantly move the rear bag after each shot to get it pointed back at my target.
Finally, I decided to try a position that just felt good to me. Body angled to the rifle, right leg straight back in line with the barrel, left leg bent at the knee with my toes on the ground, which gets part of my torso off the mat, the butt touching my shoulder. Voila: I was comfortable; it was repeatable, and re-aiming was easy. Light cheek pressure (almost none), light grip, butt barely touching my shoulder. The recoil moves my shoulder back and I let it move as much as it wants. I can reload, push the rifle forward with my shoulder, and be back to where I want before the target comes back up.
The most important thing it to try different positions until you find what is comfortable and repeatable for you, and which enables you to get the rifle back on target with a minimum of fuss. People have different bodies and different notions of comfort. Experiment and find what works best for you, without feeling like you have to do it a certain way.
Your body position will depend in part on the height of your rear bag. A taller bag forces you to raise your shoulders and head, so your back is arched inward. The rifle’s stock design will also play into this. With one rifle, I’m forced into the curved position; with the other, I’m flatter. I prefer the latter, but you may not.
Also, you have to decide how to position your support arm. Elbow further forward from your body (which will lower your position) or further in toward your body (which raises your position). I like the elbow further out, as it makes me flatter and more relaxed, but the other way may work better for you.
The OP asked a great question about whether the head should be tilted back or down. In my opinion, there’s no “best” way here. Try both. But be aware that consistent cheek pressure is absolutely critical. Choose the method that is most comfortable for you and enables consistent cheek pressure from shot to shot.
Bottom line: there are various ways of positioning your body and the best way is one that’s comfortable, repeatable, and works best for you.
Dave Rabin