Have you thought about just using Alpine? Do you need Livewire for it? This is a little sloppy, someone may have a cleaner approach, but this might work for you and requires far less code.
<div x-data="{ active: 'chip0' }">
<span id="chip0" :class="active == 'chip0' && 'highlight'" @click="active = 'chip0';">chip0</span>
<span id="chip1" :class="active == 'chip1' && 'highlight'" @click="active = 'chip1';">chip1</span>
<span id="chip2" :class="active == 'chip2' && 'highlight'" @click="active = 'chip2';">chip2</span>
<span id="chip3" :class="active == 'chip3' && 'highlight'" @click="active = 'chip3';">chip3</span>
</div>
<style>
.highlight {
background: yellow;
}
</style>
If you didn't want to have to hardcode any of the comparisons, you could do this...
<div x-data="{ active: 'chip0' }">
<span id="chip0" :class="active == $el.id && 'highlight'" @click="active = $event.target.id;">chip0</span>
<span id="chip1" :class="active == $el.id && 'highlight'" @click="active = $event.target.id;">chip1</span>
<span id="chip2" :class="active == $el.id && 'highlight'" @click="active = $event.target.id;">chip2</span>
<span id="chip3" :class="active == $el.id && 'highlight'" @click="active = $event.target.id;">chip3</span>
</div>
<style>
.highlight {
background: yellow;
}
</style>