I'd take this concern seriously if we weren't 50 years or more into carefully chosen and promoted intentionally divisive issues shaping what everyone thinks of politics.
Abortion is exactly the kind of issue that has zero impact on those in power, who can always go to another country, but influences elections.
In terms of shaping views, welfare was designed to allow single mothers to stay home and raise their kids. Yet by twisting the issue people no longer support the idea.
Unions are no longer seen as something that helps 'you', they now help 'other' people.
Clearly some people care about the issue and many say they care about it. But in terms of overall importance the tax bill for example got vastly more support. So, I suspect actual support is rather low.
In other words people might vote yes, yet at the same time prefer it not come up for a vote.
I'm not sure I get where you are going. It might be a divisive issue but saying that simply because it comes up and you think something else is more important doesn't mean it is being used just to be divisive.