What are the UART voltage levels for the RN4020?
While it's not explicitly mentioned in the datasheet the typical application schematic seems to indicate it is compatible with 3.3 V logic because the following nets are connected directly to the RN4020 module, although you wouldn't want to exceed the Vdd supplied to the module which is 3.3 V in this case as well:



The I/O pins you've mentioned also include analog I/O so are probably connected directly to an internal ARM processor running at around 1.6 V. I've seen that configuration on other wireless modules before and the minimum supply voltage of 1.8 V would seem pretty much in line with it having an internal low-dropout regulator.

The datasheet is marked as "advance information" so while I think powering the whole system from 3.3 V as per the application schematic should be safe enough if that isn't suitable for your particular application it may be worth enquiring further with Microchip.