Is it safe to implement a split power supply from two identical AC/DC adapters?
This architecture would work if the wall adapters are isolated (some wall adapters aren't on purpose). No power applied (offline), connect the - terminal of the primary to the - terminal of the secondary, and test the resistance between the remaining + terminals.
HOWEVER when the Earth is isolated/not present (2 prongs or 3 prongs with the earth prong being made out of plastic for example), you are giving up on a very important safety feature: residual current devices. They cut off the supply when they detect a leak to Earth (a person or a short to case) which can be lethal. You NEED to make sure the secondary voltages are inherently safe for you to accidentally touch, given the environment. The voltage between V+ and V- will be twice V+, in particular. Normally, the isolation would prevent any person from closing the circuit rendering it safe, but if not tied to Earth the voltage can float quite high and a fault would be dangerous.


Edit/note: The safest is 2 terminals plus Earth connected to case, and Line-Neutral of primary isolated from secondary. This way even if there is a fault, the residual current devices of your house will trigger. 2 terminals which are isolated from the primary, Earth absent, is safe in the absence of fault but dangerous if there is one. 2 terminals which are not isolated from the primary, Earth absent, is generally very risky: consider a very simple voltage divider as an example, and imagine the bottom one breaks - the entire line voltage is present at the output...


AND protect the circuit against overcurrents/short circuits if the wall adapters do not include any, to prevent fire. 
The following is circuit specific: some circuits will behave dangerously if one of the supply rails is missing. Since it's very likely that one adapter may be plugged without the other, this should be taken care of. Say, with some logic that inhibit both if one of them is missing.