Here is an updated plunker.
To make this work, you need to make visible a property of the data item. Then, you can toggle its state instead of just loosely scoped values.
<body>
<h3>using ng-repeat:</h3>
<p>(click a name to cross it out)</p>
<div ng-init="peeps = [
{name:'John', age:25, gender:'boy', visible:true},
{name:'Jessie', age:30, gender:'girl', visible:true},
{name:'Johanna', age:28, gender:'girl', visible:true},
{name:'Joy', age:15, gender:'girl', visible:true},
{name:'Mary', age:28, gender:'girl', visible:true},
{name:'Peter', age:95, gender:'boy', visible:true},
{name:'Sebastian', age:50, gender:'boy', visible:true},
{name:'Erika', age:27, gender:'girl', visible:true},
{name:'Patrick', age:40, gender:'boy', visible:true},
{name:'Samantha', age:60, gender:'girl', visible:true}
]"></div>
<ul ng-init="visible = true">
<li ng-click="peep.visible = !peep.visible" ng-class="{'strike': !peep.visible, 'none': peep.visible}" ng-repeat="peep in peeps">{{peep.name}}</li>
</ul>
<div>
<span>select only:</span>
<select ng-model="selectedPeep" ng-change="peeps[selectedPeep].visible = !peeps[selectedPeep].visible">
<option ng-repeat="peep in peeps" ng-value="$index">{{peep.name}}</option>
</select>
<span>{{changed.name}}</span>
</div>
</body>