Well soon assuming I did agree with your hypothesis that the left wing supporter seems less than enamoured with the British way of life, it may be because of the inequality that is rife, the lack of housing, the attack on the NHS etc. It isn't because we abhor the British way if life, just the way it has been hijacked by the far right. The British way of life will continue just the level of unfairness will be diminished.
With regards to the monarchy, they are an anachronistic result of our history, and largely seen as an irrelevance by many, but by no means all those on the left, many on the right feel the same way - look across the Atlantic and you will find 200m of them!