The case is being heard in the UK so I'm only talking about the UK. Unlike the US, court appointments in the UK are not political and not for a life long term. Even the public image of a judge as being conservative/liberal is not something really seen here.
The politics of appointments in the UK is less obvious than that of the US, but it is there. The Secretary of State for Justice, a member of the cabinet appointed by the PM, has veto power over appointments to the UK Supreme Court.
Good point although I think that mechanism is rarely used and highly scrutinised when it is. The government has lost several high profile court cases in the last few years which I doubt would happen in a more politicised system.
