Usually the larger the aircraft, the higher cross wind component is allowed for an autoland (larger mass, larger inertia)..I believe it's 25knots for the 777 and "only" 15knots for the 737. However a 15kt crosswind is usually quite strong, since ATC will assign you a runway where the winds will be more "head on" with the aircraft
Let's say you are cleared to land at 24R,the wind is coming from 275 at 30 whopping knots, by using a chart I can determine that the crosswind component is just 18 knots...but no conditions for autolanding a 737 though
But in most cases, it's not the wind that forces you to do an autoland, it's the visibility. The max. allowable crosswind component for MANUAL landings are way higher compared to autolandings. The 777 can have a crosswind of 45kts, and still land legally (if the runway is dry)...but I doubt many would even try that, I don't think the rudder is FBW
My advice is just to keep on practicing Jr. Crab into the wind and keep that localizer needle centered, and follow the FD commands!