Two inches is an odd size for framing material. It might be a 2x4 set flat, which is actually 1 1/5 inches thick.
It is highly likely that this framing member is attached to the cinderblock at several points. If this is so, there is no issue with just attaching to the framing.
If the framing is not attached to the cinderblock, it would be significantly less sturdy than a conventional wall in which the 2x4s are set on edge. In standard framing you are attaching to an edge that runs 3 1/2 inches deep. That means your setup would be more prone to bowing, especially in the middle, under the weight of a heavy load.
There are many factors that go into whether or not that would pose a practical problem. How heavy a load will be on the wall units? How far from the wall do the units extend? How many studs can you attach to for each mounting device or unit? How close to the ceiling and floor (the strongest areas) are the principle attachment points?
If you cannot determine whether the studs are attached to the cinderblocks, I would probably try to anchor into the cinderblocks, at least at several points, but not necessarily every point of attachment.
SUPPLEMENT
There are two forces at work in a wall hanging - downward and outward. Assuming the fastener is in a solid medium like framing wood, the downward force, shear force, is controlled mostly by the the ability of the fastener to resist being broken across its circumference. In general, standard screws and bolts are plenty strong.
The outward force is largely controlled by two things - the strength of the fastener in the support material and the rigidity of the support material. Again, standard screws or bolts in wood are up to it (these systems are designed for that). The problem, if any is the ability of the framing to stay in place.
The main support mechanism is near the top of the unit (that horizontal hanging strip), and the framing near the ceiling is fairly secure because the vertical studs are attached (hopefully) to some sort of top plate, spreading the load.
You are probably safe going into the wood. But if it were me, I would not rely on probably, and I would anchor into the blocks in at least three places along that top hanger. If they are hollow blocks, I would try to hit a hollow and use a toggle type anchor. If solid, an expanding masonry anchor.
You could search for something called a block and tackle. This is a rope and multiple pulley system that gives you a mechanical advantage over a single pulley making it much easier to hoist the tire into place.
You should consider mounting four hooks on the ceiling overhead so that the block and tackle can be moved to the position where the tire will be resting on the shelf. The upper "hook" could even be a bar or pipe affixed to the ceiling in such manner that the top securing point for the block and tackle can be slid back and forth so that it can be pushed into position before hoisting each tire.
Best Answer
If the canoe is getting in the way, can you not put a second pulley wheel with the cord over it off to the side so you can pull the cord from the ground? Then you can just use a standard cleat.