Moore machine state diagram and state table
the output only depends on the current state Then why does the table for states F and H say the output is independent of the input?


Because if it depends only on the current state, then it can't also depend on the inputs. 

The inputs determine whether you get to a certain state. But after you're in that state the output only depends on the state. Assuming a typical clocked design, the output doesn't change instantly if the inputs change before the next clock edge. And it only changes at the clock edge if the changed inputs lead to a new state.