> as though the two things, a person's character and their ideas, are somehow not connected.I somewhat agree with you that the character of a person can be inferred by the ideals they claim to hold. Perhaps it would be more accurate to say that, given the context of the worldview held by the speaker, you can infer positions that person might take on other issues of the day.
Understanding the worldview of the speaker is incredibly important when making character calls. I've found that people will attempt to reveal their character to you in subtle ways, often in an attempt to see what positions you claim to hold in response. The ideals they claim to hold often mean very different things for their character depending on their worldview.
Example: I've found that when interacting with people who have grown up in black culture, when they make a statement against the ownership of guns, they're actually signaling to you that they don't believe in the unjust use of violence. In white culture, revealing a pro-gun stance says more about their belief in the role of the individual in relation to the government. Confusing one for the other will result in a very unproductive conversation.
People tend to interpret other's words outside of the context of the speaker's actual worldview. My understanding is that this is the problem that 'attacking the person's ideas, rather than their character' tries to solve.
Full disclaimer, I grew up in a very conservative circle(The kind that didn't vote for, and generally has a strong distaste for Trump), and as a result I have a very good understanding for how their ideas tend to be generated. I can say with confidence that many of these people have outstanding moral character, but would also be condemned by those in more liberal circles.(Granted, the conservatives I know are absolutely guilty of the reverse)