Why is a centrifugal compressor in aircraft engine less susceptible to stall and surge?
The reason comes down to the principle of operation of the compressors - a centrifugal compressor, as it's name implies, just spins around really fast, and the centrifugal force compresses the air. As you can see in the image below, the vanes of the impeller of a centrifugal compressor just help push the air around in a circle (unlike an airfoil) and centrifugal force does the compressing:
The centrifugal compressor is circled in blue. As you can see, when the impeller rotates, it pushes air to the side.


Image source - https://upload.wikimedia.org/wikipedia/commons/6/6f/Saturn_MD-120_cutaway.jpg

An axial compressor has blades that work like little rotors (which are really just rotating wings) - the rotors accelerate the air, and the stators slow the air down again, using that kinetic energy to compress the gas. Just like wings, these blades can stall and lose function whenever the input flow is disturbed enough (such that the local angle of attack of a portion of the blade is too high for the given local flow conditions). This stall can then potentially spread to other blades, or to the entire engine. 

As you said, the vanes of an impeller in a centrifugal compressor don't work like airfoils (instead, they kinda just rotate and push air around, kinda like a turnstile), so if they encounter airflow disturbances, they won't stall like an airfoil would. Of course, if said airflow disturbance is something like severely restricting airflow, the compressor will surge, but this is considered rare in practice.

Therefore, it's much easier to get an axial compressor to surge or stall (just by disturbing the airflow a lot) in comparison to a centrifugal compressor, which requires airflow to be restricted.