ADC input range vs sensor output range
Firstly the workings of the current sensor; -50 amps corresponds with a voltage output level from the ACS758LCB-050B of 0.5 volts, 0 amps is 2.5 volts and +50 amps is 4.5 volts. This ties in with the 40 mV/A sensitivity stated. It's output cannot fall to 0 volts nor rise to 5 volts.

Next the RMS to DC converter. This picture from the data sheet shows how it interfaces to signals: -



Text below slightly edited to fix error

The supply would be 5 volts and 0 volts and half the supply voltage (2.5 volts) is applied to the IN2 input. This makes it relatively easy to interface with the ACS758LCB-050B because it naturally produces a quiescent DC level of 2.5 volts. But you have to limit the input voltage range to a peak voltage of 1 volt: -

VIMAX Maximum Peak Input Swing (Accuracy = 1%) 1 volt minimum


So you need to reduce the output swing of 0.5 volts to 4.5 volts from the ACS758LCB-050B to 1.5 volts to 3.5 volts for the LTC1968.


  the output of the RMS-to-DC convertor is also 0 - 5V.


No it isn't: -

VOMAX Maximum Differential Output Swing 1 volt guaranteed


That swing can be manipulated to higher or lower absolute levels by the RTN pin but the swing is +1 volts. So, for best accuracy with your ADC choose a voltage reference that gives close to full scale with an output swing from the LTC1968 of +1 volt.