An argument or function DATE has wrong data type will not resolve

Devtr I see the issue, sometimes _First_Arr_Date is BLANK.

Try this:

LY_Past_Res_Rooms = 
var _First_Arr_Date = FIRSTDATE('FutureReservations'[arrival_date])
return
if(_First_Arr_Date = BLANK(), BLANK(),
        var _LY_First_Arr_Date = DATE(YEAR(_First_Arr_Date)-1,MONTH(_First_Arr_Date),DAY(_First_Arr_Date))

        var _Last_Dep_Date = LASTDATE('FutureReservations'[departure_date])
        var _LY_Last_Arr_Date = DATE(YEAR(_Last_Dep_Date)-1,MONTH(_Last_Dep_Date),DAY(_Last_Dep_Date))
        var _Result = CALCULATE(COUNT('Past_Reservations'[rate_cat]),
                FILTER(ALL('Past_Reservations'[arrival_date]),
                        'Past_Reservations'[arrival_date]>=DATEVALUE(_LY_First_Arr_Date)
                        &&
                        'Past_Reservations'[arrival_date]<DATEVALUE(_LY_Last_Arr_Date)
                        &&
                        'Past_Reservations'[arrival_date]<>BLANK()))
        return
        _Result
)