General purpose equipment can be acceptable at .001 inches per inch of separation. These are just rules of thumb. Misaligned couplings pass reactionary loads to the shaft and bearing system of the connected equipment. The greater the misalignment the greater the reactionary load. Different types of couplings have different reactionary loads.
Reactionary loads are the cause of the problems.
Allowable misalignment depends on the coupling design. Elastomeric couplings accommodate misalignment by distortion of the elastomer. They can be misaligned in both the offset and angular mode with a single flex plane. Other couplings can only flex in the angular mode so they must have two flex planes to accommodate offset misalignment. The spacing of the flex points determines the amount of offset misalignment capability of an individual coupling.