You have two situations: the breaking strength (or safe working load, whichever concerns you) of the
line through the block and tackle and second, the breaking strength (or safe working load of the mechanical components, if that's what you are working with).
Count the
lines on the movable block... that gives you the mechanical advantage. Thus if you have 5
lines to the movable block and you are lifting 100 lbs., you will need to apply 20 lbs. pull to lift the weight. Forget the friction of the bearings, etc. For the accuracy of a practical situation, they will be relatively small if you have lubricated the sheeves (rollers). The load applied to each part of the
line is 20lbs. in this example.
For the mechanical side, each component has a breaking strength or safe working load. Without knowing the characteristics of each metal, each plastic, and size of each component, you or I cannot really calculate the strenght of each component. If you will determine the manufacturer and model of the blocks, hooks, etc., you probably can go to the manufacturer's catalog and see what the safe working load or breaking strength is for that component. The weak component is your safe working load for the system. Sometimes blocks,
shackles, and the like give breaking strength also. Generally, the breaking strength will be on the order of 2.5 times the safe working load for mechanical components. For line, it is about 15% of breaking strength. These are only approximations, and condition of the components can reduce this considerably, so care is needed not to push the loading to the limits. Also, if you are picking up heavy loads, make sure that your lines are in good shape and that you know the rating for the lines and also inspect the mechanical components for wear or distortion from loading or bending. If the components are not in good shape and you push the loading too far, you may get an unpleasant surprise. Please proceed cautiously, and if you use the above information, you do so at your own risk. (I don't want anyone saying you told me it was safe and therefore my disaster is your fault).
Also, the manner in which the load is applied is critical. If the load is dropped on the block and tackle, or the slack is drawn out quickly, you move into impact loading. When you do that, stress loading goes up rapidly many times over, so a system that would have held together if the load was applied gradually might well fail.
If you think you are getting close to the breaking stength, up size your block and tackle several times over. It will be cheap comparied with the consequences otherwise.
You original question related to a soft
shackle. That is not like a block and tackle. As I understand it, a soft
shackle is a piece of line with a knot in one end and a small loop (generally spliced) in the other end and you
shackle components together by putting one end of the line through/around items to be shackled together, then pass the knot throught the small loop, which is sized so the knot just passes through. When the load is applied, the system holds together because the knot slides up against the end of the loop. The load that such a system will hold far, far less than the breaking or working strength of the line (or multiple lines) in the soft shackle. Personally, I would not use such an arrangement in a high loading situation, except that I had tested the actual soft shackles in actual loading situations. I expect that commercially made ones have been tested and rated accordingly. Generally knots reduce breaking strength by about 50%, but the way a soft shackle is loaded is more likely to fail by shearing or tearing of the shackle. This would be a partial tearing of the shackle and would not approach the breaking (tensile strength) of the line comprising the shackle. Also, allowable shear stress loading of most materials is considerably less than tensile strength. Also, ropes have certain elastic properties and stretching is likely to be heavily involved in the failure of your soft shackle.