Doing something which Hashem hates is not the same as hating Hashem.
I’m alleging that they hate Hashem, because they hate the Jewish people.
Everything done is mekadesh sheim shmayim
Well, everything eventually leads to kiddush Hashem. In their case, when we are eventually yatzu v’ra’u b’pigrei ha’anoshim haposhim bi, ki solaatom lo samus v’isham lo sichbeh