I don't know this bishop, so I can't say anything about his politics, but I would imagine the number of Catholics who are religiously opposed to birth control who actually voted for Obama could dance on the head of a pin.
I also know from experience and from reading that the number of churchgoing (active) Catholics who voted for Obama are dwarfed by the same demographic who vote life (which is typically Republican, but certainly not Obama).
I don’t know where you get your opinion, but I disagree with it.
Black Catholics voted for Obama in spite of their anti-abortion stance if they had one. Many Democrats voted party and voted Obama in spite of being Catholics.
IMO few Catholics are very religious any longer with probably less than half who bother to go to confession any longer.
Most Catholics use some form of Birth Control NOW in spite of the Church’s edict on it.
I like the way you think, but I believe you are wrong.