The reason there is still disagreement as to what constitutes measurement is that it makes no experimental difference according to quantum mechanics. The way QM works under the Copenhagen interpretation is that you have to split the world into two parts, the “observer” or measurement device, and the “observed” or the particles you’re measuring.
The measurement device is assumed to behave classically. The particles in the observed system are in a superposition of states described by the wave function which keeps evolving until it interacts with the classical measurement device. The question is where to draw the line. You could consider a photon to be the observed system and an atom to be the measuring device, but you can also consider the photon-and-atom system as in a superposition of states, and take a Geiger counter to be the measurement device. So there is this von-Neumann chain, going from elementary particles to Geiger counters to human beings, and we have to decide where to cut it off.
Von Neumann proved in his famous "Bible" of QM that regardless of where you cut the chain, you would get the same experimental results. But he argued that wherever you cut the chain you have things made out of particles on each side of the cut, so there’s no principled way to place the cut in the middle. So he decided that you should place the cut between the human mind and the human body, because he believed that the mind is non-physical. Hence "consciousness causes collapse" was born. Nowadays, the most popular view is decoherence, where there is no real collapse, it's just that when you have a large number of particles in the environment interacting with the system, the wave function becomes smeared out and looks like it has collapsed. So decoherence gives us a reasonable place to cut the chain, when the number of particles involved reaches a critical number so that interference effect become negligible.
