The crossfeed valve on the 737 is checked for ETOPS in the cold soaked condition - if the initial leg is non-ETOPS (i.e. an overland segment before heading into the ETOPS sector) then it can be done at the end of that leg, otherwise it is done before descent on the previous leg.
The 737 performs this check because it is fitted with a single crossfeed valve. The 767 (which is fitted with two valves) isn't required to perform a check (at least when I was flying ETOPS in Australia).
In the same sense, the 737 runs the APU throughout the ETOPS sector, to guarantee two sources of power after an engine failure - but the 767 doesn't need to, as it has a RAT (Ram Air Turbine).