The lower judges have nothing to do with politicizing the office. Even if every judge was appointed, in this partisan environment it would NEVER be about qualifications. Its silly to suggest that if only there were no judge elections then the next time the president nominated a supreme court justice the senators and representatives would suddenly quiz them on legal knowledge as opposed to their stances on hot button issues. Look at ANY office appointed by politicians, its ALWAYS about politics whether it be a judge a cabinet member or a head of a department.
That must be a problem peculiar to the US, because here most judicial appointments are certainly not political decisions, though they are carried out by the executive (there is something seriously wrong with an appointment system in which nominees to the judiciary are grilled on such hot button issues as you say, certainly, but that's a reflection on the US' peculiarities, not on the general concept of appointing vs. electing judges). On the other hand, judges who survive from election to election are always going to be political, by the very nature of their tenure. The entire basis of their authority becomes political when you are bringing elections into it. Judges become explicitly political figures. I don't think it is unreasonable at all to say that the politicising of the judiciary in such a way creates an environment in which judges are essentially forced into adopting some sort of political identify, and operating along those lines.
It seems odd to argue that appointments are bad because they might lead to the politicisation of the judiciary, when elections guarantee that. Even if a judge is elected because they've promised to be as objective and non-partisan as possible, then that is nothing more than a political position.