I think you overestimate just how much the average person cares about politics. We talk about it here, on a daily basis, and that makes us believe that everybody is as vested as we are.
In reality, there's a ton of people who don't give a single care about such things. They don't vote. They don't get into arguments with friends and family about it. They just go about their lives trying to make enough money to keep eating and keeping a roof over their heads.
There are absolutely going to be members of the jury pool who will be biased one way or the other. It's up to the lawyers to try and weed out any that they feel are biased, but in the end, I think that percentage is smaller than you imagine it to be.
I've been in a court jury a few times. In every case, they instruct the jury up front that it doesn't matter what you believe about the trial, the defendant, or the world outside. All that matter is the facts of the case that are presented in that court room. I was on a jury where a guy was being charged with gun possession and he was a former felon who could not own a gun. Personally, I though he kinda got a raw deal. I could think of several ways that the defense could have argued a reasonable doubt case. They didn't do that though. We all voted to convict. The jury has to vote based upon what is presented. Not what they feel.
I have faith that the jury they use will be able to do that. Maybe I'm wrong, but my experience tells me that it should be possible.