Haskell, 54 50 bytes
t a=or[and(zipWith(<=)`f`tail$a)|f<-[(=<<),(<*>)]] Usage example: t "defggh" -> True. Try it online!.
Maybe using sort like may other answers is shorter although it requires import Data.List. Here's a different approach:
For every function f from [(=<<),(<*>)], calculate and(zipWith(<=)`f`tail$a) and require any of the results to be True. The functions are
((=<<) (zipWith(<=)) tail) a ((<*>) (zipWith(<=)) tail) a which both perform comparisons of neighbor elements of the input list a with <=, but one with the arguments flipped resulting in a >=. and checks if all comparisons are True.