Changing directory with if else condition

You need to use a variable's name in the for loop header. You used $file in your original question, i.e., the variable file's value.

You are also doing things a bit complicated. To run a command with a temporarily changed working directory, you may use a sub-shell.

( cd Em1 && month_range )

The working directory outside of the sub-shell is not affected by the cd inside the sub-shell. It's unclear what your cd_ret function is doing, so that's another possible source of errors. If you can't do it this way, for example, if month_range is setting variables that need to be visible in the original scope, then use

cd Em1 && { month_range; cd -; }

The above would cd into Em1, run the month_range function, and cd back, assuming month_range does not do further calls to cd. If month_range does use cd, then save the current working directory in a variable and use that instead.

wd=$PWD; cd Em1 && { month_range; cd "$wd"; }

The above assumes that month_range does not change or unset the wd variable.

Your use of awk is problematic as filenames on Unix technically may contain newline characters. It would be better to use a parameter substitution.

em=${file%%[.-]*}

The above chops off the value $file at first - or . character and assigns the resulting string to the variable em.

This leaves you with the following:

em1=first
em2=second

for file in *; do
        em=${file%%[.-]*}

        if [ "$em" = "$em1" ]; then
                ( cd Em1 && month_range )
        elif [ "$em" = "$em2" ]; then
                ( cd Em2 && month_range )
        else
                echo 'Nothing to do'
        fi
done

or

em1=first
em2=second

for file in *; do
        em=${file%%[.-]*}

        case $em in
                "$em1") ( cd Em1 && month_range ) ;;
                "$em2") ( cd Em2 && month_range ) ;;
                *) echo 'Nothing to do'
        esac
done

or, without extracting em from $file at all,

em1=first
em2=second

for file in *; do
        case $file in
                "$em1"[.-]*) ( cd Em1 && month_range ) ;;
                "$em2"[.-]*) ( cd Em2 && month_range ) ;;
                *) echo 'Nothing to do'
        esac
done

or using bash syntax,

em1=first
em2=second

for file in *; do
        if [[ $file == "$em1"[.-]* ]]; then
                ( cd Em1 && month_range )
        elif [[ $file == "$em2"[.-]* ]]; then
                ( cd Em2 && month_range )
        else
                echo 'Nothing to do'
        fi
done

If this then does what you intend depends on the month_range function or script.