Input impedance of a non-inverting op-amp
Feedback always influences the input impedance of an amplifier. However, it depends on the kind of feedback. When the feedback signal adds with the input CURRENT (example: inverting opamp) the input impedance is reduced by the factor (1+loop gain). However, when the feedback signal is superimposed on the input VOLTAGE (example: non-inv. opamp) the input impedance is enlarged by the same factor (1+loop gain). 

This can be explained simply as follows: The opamp reacts upon the voltage difference between both inputs. The input resistance can be modelled as a resistance between these inputs. Now - when due to the feedback action the voltage at the negative input node follows the voltage change at the pos. input node, the voltage difference across the input resistance is much smaller (if compared with the case of a grounded inv. node). Hence, the resulting input current drawn from the signal input is much smaller. This explains the increase of the input resistance due to feedback.