Regarding 'Infringe on his privacy', the unstated assumption is that "he" has a right to privacy in whatever the situation is. That may not be true in some situations therefore any limiting, undermining or encroaching would not constitute infringement. The same holds true if you substitute "right to keep and bear arms" for "privacy".
So those bombasts who start sentences with "I don't want to infringe on anyone's rights, but ..." are doing exactly that.
Not necessarily. Someone who says "I don't want to infringe on anyone's rights, but ..." may just be trying to figure out where the right of one person begins and the right of another ends.
Some people might maintain the “right to keep and bear arms” (which right “SHALL NOT be infringed”) does not include keeping and bearing arms on the property of someone else who has not given permission to do so, and that doing so anyway is an infringement of the person's property rights. If so, prohibiting keeping and bearing arms on private property is not an infringement of the right. Some people might maintain otherwise.
A person trying to figure out where the right of one person begins and the right of another ends might begin with the statement "I don't want to infringe on anyone's rights, but ..."