For Vue.js 2 you could have the active class be dependent upon a boolean data value:
<th
class="initial"
v-on:click="myFilter"
v-bind:class="{ active: isActive }"
>
<span class="wkday">M</span>
</th>
methods: {
myFilter: function(){
this.isActive = !this.isActive;
// some code to filter users
}
}