It is a good question . . . .
In a high-wing aircraft, the flaps reduce the airflow over the vertical stabilizer and rudder, making them less effective. I always had better luck with crosswind landings in 172s when I backed off on flaps.
It depends on the crosswind. If it is only a few knots, backing off on flaps may not help appreciably. But, with five or more knots of crosswind, you'll see the difference.
You may not want to use full flaps during an approach in gusty winds and/or turbulence. Backing off on flaps will improve controllability. You want to carry more speed into the approach - perhaps half to all of the gust factor - and fly a powered approach all the way down. Less flaps with more power and speed will, again, improve controllability. With reported shear, you definitely want to carry more speed.
If you have doubts that less flaps and/or more speed will cause you problems getting in on your runway, look at your landing chart. See how headwind component shortens your landing distance.
Hope that helps a little more.