I cannot think of many ways in which a person's politics might affect whether they remove their shoes at the door or whether they prefer visitors to remove their shoes.
I suppose many Conservative party supporters in the UK are likely to be upper middle class and thus would never ask guests to remove their shoes. That is just not done in respectable society here.
I expect environmentalists are probably more likely to have a shoes-off policy, as they worry a lot about pollution and pesticides. Those things can be picked up by one's shoes.