Differential input voltage of op-amp with feedback
The maximum input differential voltage is a breakdown rating on the input stage structure and cannot be ignored; it is in the datasheet for the very good reason that exceeding this may damage the device.

If you power this device from (for instance) +5V and ground, then the output can only slew to within a few millivolts of ground, so if your input goes to -1V, you will definitely be violating the maximum rating of the device.

If you want to convert a bipolar square wave to a unipolar one, a series diode (to prevent the input going negative) and a comparator may serve you better.

Note that the gain bandwidth product of an amplifier is not directly tied to slew rate, which determines what the output looks like. To remain within the small signal region (i.e. the output is not in slew rate limit), the following rule applies:

fmax =  Sr/2πVp where fmax is the highest frequency in your signal, Vp is the peak voltage at the output and Sr is the slew rate from the datasheet.