Most people their opinion is based on feelings, which often exist because of a screaming idiot on TV.

For example, my mom wants Islamic people out of this country, because they are criminals and do not belong here. She's lived her entire life in white neighborhoods, never had any experience with crime happening to her by anyone, but she feels this way because of a right wing politician screaming on TV. I have no issues with Islamic people while I live in a neighborhood full is mixed cultures, including many Islamic people. Any factual counter argument I present to my mom feels for her as a personal attack, because I'm attacking her feelings with logic, so the counter attacks with bullshit like "you have no respect to your parents/elders", "I'm not allowed to say anything anymore these days", "what do you know, knowledge comes with the years, I'm older so I know better". She assumes I'm just attacking her extremist comments because of puberty (I'm 37) and to make her feel bad.

I feel like she represents most people, as most people; assuming what people say on TV / internet is true, creating a feeling and opinion based on that which is carved in stone, seeing any counter argument as a personal attack, throwing counter attacks based on words put in other's mouths because attacking that is much easier then properly constructed factual counter arguments (because they don't have any).

FYI I ended all contact with my mom. She's angry about that too, she lacks the ability to see her actions have consequences. Again, like most people.

You say "An opinion with zero relevance or weight is absolutely useless." That is completely true. But those opinions do make people vote in a certain way. They do fuel hate. They do spread fake news. They ruin our society. So even though they have zero relevance and weight, they are super relevant and carry a lot of weight at the same time.