You can't force other people to find your values important. You can't twist human psychology so that 'empathy' constantly will overrule self-gain.
What you can do is compromise. If the democratic party were pro-guns, pro-rural development, and also pro-abortion then you'd be surprised to find how many people would stand with them.
Unfortunately this is the core of the issue. That first sentence should really read "What the democratic party can do is compromise" for the second sentence to follow. As a voter in the United States you are personally forced to compromise. In order to choose the lesser of two evils you need a developed sense of empathy and morality, and based on the comments in the original article many people seem to be missing this.
Reform of the democratic/republican parties (someone as compromised and mentally unstable as Trump being elected is a serious republican issue) is an entirely different organizational problem that can only be done by party insiders.
The difference is they would be wrong because violence against LGBT people is much more widespread than Islamic terrorism in the US. Racists and gay-bashers will literally use any issue in place of "Islamic terrorism" to denigrate gay and black rights and it is disgusting and they should absolutely be insulted and marginalized for it.
Competent people can do more than one thing at the same time.