Recharging of Inverter Batteries
Is it possible for some reason I can be able to safely connect two charge controllers (who draw their solar power from the same solar panel array) to charge separate/independent batteries?


Generally, yes.
There may be some interaction in some cases but two controllers fighting for energy is little different than a panel providing variable energy as insolation changes.   

It is possible that PWM noise from one controller MAY affect the other.
Worst case, adding a large capacitor at the panel output may be useful.