If you put flap down then stability with respect to a crosswind gust is reduced for one additional reason not yet mentioned. A gust from an angle to one side will lift one wing because it will hit the whole of that wing, but the other wing will be shielded by the fuselage an only encounter the gust at the tip section. If flap is used it increases the lift on the inboard section of te wing only. Therefore the imbalance in lift will be greater, as this is the area not producing additional lift on the down-going wing.
Turbine is correct in that in a steady crossswind full flap is a better technique, for thereason he gave. The critical period is the time between kicking off drift and touching down. At this time you will start to drift sideways, so you want to minimise the time spent in this condition.