Vue.js toggle class on click

You could have the active class be dependent upon a boolean data value:

<th 
  class="initial " 
  v-on="click: myFilter"
  v-class="{active: isActive}">
  <span class="wkday">M</span>
</th>

new Vue({
  el: '#my-container',

  data: {
    isActive: false
  },

  methods: {
    myFilter: function() {
      this.isActive = !this.isActive;
      // some code to filter users
    }
  }
})

Without the need of a method:

// html element, will display'active' class if showMobile is true
//clicking on the elment will toggle showMobileMenu to true and false alternatively
<div id="mobile-toggle"
 :class="{ active: showMobileMenu }"
 @click="showMobileMenu = !showMobileMenu">
</div>

//in your vue.js app
data: {
    showMobileMenu: false
}