So your edit does address a critical point. A member of a certain ideology does not make me automatically disqualified from acting as a juror. Taking your intent over words, I'm going to substitute in Walter being an avid lover of pineapple pizza to demonstrate with less charged opinions. For the record, Pineapple Pizza is my favorite thing in the whole world, and my favorite breakfast food is cold leftover pineapple pizza.
Now, in the grand scheme of things, Pineapple Pizza will not be critical to most cases a jury will be asked to hear, so... assuming this is a world where the war between Pineapple Pizza lovers and Non-Pineapple Pizza lovers is at a level where expressing support for Pineapple Pizza will get me canceled, dropped from social media, and have late night comedy mocking me endlessly if I openly said so... my belief shouldn't disqualify me from hearing evidence in a murder trial where pizza does not factor into the events of the murder.
Now, where this becomes a problem is lets say the person on trial is a pizza delivery boy, who killed the victim because the victim ordered a Pineapple Pizza. As a Pineapple Pizza lover, I would probably be a poor jurist because how dare someone kill over their refusal to admit the supremacy of Pineapple and Canadian Bacon as pizza toppings.
The reason why this would be undesirable is that my disagreement with pizza boy over pizza might blind me to his valid defense: He delivered the pizza and called his girlfriend, and proceeded to talk with her on the phone while he returned to the pizza shop, where his boss told him to get off the phone and because it was a slow night, he stayed at the pizza shop for the entire three hour window that the corner said the man victim could have been killed in.
In effect, now, the bias is self assessed. Walter might not think he could be that fare. Me personally, I'm not really so diehard about Pizza toppings that I can't say "Sure, the pizza boy hates pineapple on pizza and the world would be a better place without his wrong think... but I'm not willing to send him to jail because he hates pizza I like... if we have alibis for the entire time he could have committed the crime, he may be guilty of having terrible tastes... but he's not a murder.
The Jury questions usually are written in a way such that they ask if you would be unable to judge a case fairly given a certain topic. So they aren't going to ask "Do you like Pineapple Pizza?" but rather "As a juror on this case, you may be asked to hear testimony regarding the defendant's opinions on pizza toppings. Do you believe this testimony will affect your ability to render a fair verdict?"
In the case of a negative answer, it doesn't show my support, it doesn't show the opinion, it only asks will I be able to be fair in my assessment of the evidence and the guilt in the eyes of the law. If I answer yes, I'm not giving my opinion. It just means I would likely change my verdict based on the defendant's opinion. Convicting an innocent man because we do not agree on a controversial issue is juts as wrong as acquitting a guilty man because we agree.
Generally, the stuff that will get you out of jury duty the faster than having a bias against someone of a protected class is rather mundane... people who are victims of crime, people who serve in law enforcement or work in the legal system or have close friends or family that do are often out, because they are more likely to pick the prosecution's side because of bias against crime and not because of whether or not the guy on trial is actually guilty.