Shield of the Righteous’s second ability doesn’t track the blocked creature’s controller. If that creature changes controllers before its old controller’s next untap step, this ability will prevent it from untapping during its new controller’s next untap step.

When the equipped creature blocks a creature, Shield of the Righteous’s second ability doesn’t tap the blocked creature (in case it happens to be untapped due to vigilance, for example). It just causes that creature to not untap during its controller’s next untap step.

If the blocked creature is already untapped at the time its controller’s next untap step begins, this ability has no effect. It won’t apply at some later time when that creature is tapped.