Flying in LNAV , a 737 will bank with max AOB of 23 deg, or half the difference to the new heading ,if less.
In HDG SEL we tend to use 15 deg in high cruise flight and at take-off (for an engine failure less or close to V2 ) ,20 or 25 at low altitudes and in WXR avoiding. 30 deg only if necessary in WXR avoidance or LOC capture vectors.