Does the precession of Earth's axis affect our climate?
Changes in climate that can be attributed to precession of Earth's axis, over a short period, is negligible. The axis takes about 72 years to turn through 1 deg, about the normal to the ecliptic.,
In 25800 years ( called Great Year ), the axis completes one revolution about the normal to the ecliptic, maintaining 23.4 deg in-between. So, in 72 years, it turns through 72 X (360/25800) deg = 1.00 deg.