This might work
Wrap the select element in a div. give it a data element that you can increment from the livewire component
<div data-instance="{{ $iteration }}">
<div wire:ignore wire:key="w_brands">
<select id="select_brands" class="form-control ">
@foreach($brands as $brand)
<option>{{$brand}}</option>
@endforeach
</select>
</div>
</div>
create $iteration in your component. Increment it each time you change the content.
But really, as you are not using wire:model on your select element you should not need wire:ignore at all.