Not really. When "Protector of the Sanctuary" is on your side of the field, neither player can choose to activate a card effect which would force your opponent to draw a card(s).
It does not prevent a player from activating a card effect which they have no control over (such as a flip effect or mandatory trigger effect), nor does it apply to card effects with optional draw effects.
Hand Destruction cannot be activated except as a result of a conscious decision. As a result, neither player can choose to activate this card effect while PotS is face-up on the field.
In the OCG, Kuraz the Light Monarch had an optional draw effect.
When it was translated into English for the TCG, this optional effect was accidentilly mis-translated to become a mandatory draw effect.
This caused a great deal of controversy, since in the OCG - Kuraz could be activated while PotS was on the field since the controller of the detroyed card(s) was not forced to draw a cards, and could always choose not to draw.
However, in the TCG - the draw effect is mandatory and by its wording, could not be activated while PotS was on the field.
That was however, until such times as an official ruling was released which clarified how Kuraz' effect was intended to function. While the draw effect is still mandatory in the TCG, the rulings for its effect are the same as it is in the OCG.
This is a BKSS ruling which resulted due to a tranlation error. We may see the effect of Kuraz errata'ed in the future bringing its text in line with the OCG effect however I see this as unlikely.
Morphing Jar has a flip effect. Being a flip effect, the controller of Morphing Jar has no control over when (and how) morphing jar will activate.
Since flip effects activate automatically in much the same way that a mandatory trigger effect activates automatically, PotS will not prevent these effects from being activated.
It only prevents the activation of card effects which the controller of that effect has any control over.
YRK/TO/PM/Specialist LV1