I would ask why the Pope, or any religious leader should "Stay out of politics"? Religion, among other things, is supposed to offer a guide as to how one should live. I would expect them to clearly say that, "According to our holy writings and traditions, this is how one should act if one calls themselves "X".

I don't have to agree with what they say, but if I call myself an X or Y then I should follow the precepts. And if makes me uncomfortable to follow those teachings then perhaps I am not one.